perturbations of elliptic operators in 1 sided chord arc domains part i small and large perturbation for symmetric operators the first and third authors acknowledge financial support from the spanish ministry of economy and competitiveness through the severo ochoa programme for centres of excellence in r d sev 2015 0554 they also acknowledge that the research leading to these results has received funding from the european research council under the european union s seventh framework programme fp7 2007 2013 erc agreement no 615112 hapdegmt the second author was supported by nsf grant dms 1664047

duality of hardy and bmo spaces associated with operators with heat kernel bounds the introduction and development of hardy and bmo spaces on euclidean spaces r in the 1960s and 1970s played an important role in modern harmonic analysis and applications in partial differential equations these spaces were studied extensively in 32 22 18 19 31 and many others an l function f on r is in the hardy spaceh r if the area integral function of the poisson integral e t f satisfies

riemann stieltjes operators and multipliers on q p spaces in the unit ball of c n this paper is devoted to characterizing the riemann stieltjes operators and pointwise multipliers acting on mobius invariant spaces q p which unify bmoa and bloch space in the scale of p the boundedness and compactness of these operators on q p spaces are determined by means of an embedding theorem i e q p spaces boundedly embedded in the non isotropic tent type spaces t q infinity c 2010 elsevier inc all rights reserved

strong type estimates for homogeneous besov capacities capacitary strong type estimates for homogeneous besov spaces are established moreover the result is used to study embeddings and dualities of function spaces

the boundedness of riesz transforms for hermite expansions on the hardy spaces abstract let l x 2 be a hermite operator where is the laplacian on r d in this paper we first characterize the hardy spaces h l 1 r d associated with l by a new version of area integral then we use it to prove the boundedness of riesz transforms r j l j 1 2 for l on h l 1 r d moreover we characterize the hardy space h l 1 r d by r j l this gives a negative answer to a question asked by thangavelu

generalized coorbit space theory and inhomogeneous function spaces of besov lizorkin triebel type coorbit space theory is an abstract approach to function spaces and their atomic decom positions the original theory developed by feichtinger and grochenig in the late 1980ies heavily uses integrable representations of locally compact groups their theory covers in particular homogeneous besov lizorkin triebel spaces modulation spaces bergman spaces and the recent shearlet spaces however inhomogeneous besov lizorkin triebel spaces cannot be covered by their group theoretical approach later it was recognized by fornasier and the first named author 24 that one may replace coherent states related to the group representation by more general abstract continuous frames in the first part of the present paper we significantly extend this abstract generalized coorbit space theory to treat a wider variety of coorbit spaces a unified approach towards atomic decompositions and banach frames with new results for general coorbit spaces is presented in the second part we apply the abstract setting to a specific framework and study coorbits of what we call peetre spaces they allow to recover inhomogeneous besov lizorkin triebel spaces of var ious types of interest as coorbits we obtain several old and new wavelet characterizations based on explicit smoothness decay and vanishing moment assumptions of the respective wavelet as main examples we obtain results for weighted spaces muckenhoupt doubling general 2 microlocal spaces besov lizorkin triebel morrey spaces spaces of dominating mixed smoothness and even mixtures of the mentioned ones due to the generality of our approach there are many more examples of interest where the abstract coorbit space theory is applicable

square function non tangential maximal function estimates and the dirichlet problem for non symmetric elliptic operators a we consider divergence form elliptic operators l div a x defined in the half space rn 1 n 2 where the coefficient matrix a x is bounded measurable uniformly elliptic t independent and not necessarily symmetric we establish square function non tangential maximal function estimates for solutions of the homogeneous equation lu 0 and we then combine these estimates with the method of approximability to show that l harmonic measure is absolutely continuous with respect to surface measure i e n dimensional lebesgue measure on the boundary in a scale invariant sense more precisely that it belongs to the class a with respect to surface measure equivalently that the dirichlet problem is solvable with data in lp for some p previously these results had been known only in the case n 1

geometrical non linear steady state forced periodic vibration of plates part i model and convergence studies a model for the steady state geometrically non linear periodic vibration of thin rectangular plates under harmonic external excitation is presented the equations of motion in the time domain are derived by applying the principle of virtual work and the hierarchical finite element method hfem these equations are transformed into the frequency domain by the harmonic balance method hbm and are solved by a continuation method the convergence properties of the model are discussed by applying it to isotropic and to composite laminated plates

orlicz hardy spaces associated to operators satisfying bounded h functional calculus and davies gaffney estimates abstract let x be a metric space with doubling measure and l be an operator which has a bounded h functional calculus and satisfies davies gaffney estimates in this paper we develop a theory of orlicz hardy spaces associated to l including a molecule decomposition square function characterization and duality of orlicz hardy spaces h l x finally we show that l has a bounded holomorphic functional calculus in h l x and the riesz transform is bounded from h l x to l

a symplectic galerkin method for non linear vibration of beams and plates abstract non linear free vibration of beams and plates is conservative in the sense that the total energy of the system remains constant symplectic numerical integration aims to preserve the energy momenta and area volume of the phase space and is ideal in the study of non linear free vibration in this paper the lagrangian of continuous systems is discretized by galerkin s method to obtain the discrete hamiltonian and hamilton s equations symplectic numerical integration schemes are applied to the resulting ordinary differential equations to construct the phase diagram it is shown that due to modal coupling bounded quasi periodic and non periodic free vibrations are very common for continuous systems comparison is made with the runge kutta method it is shown that the runge kutta integration reduces the total energy of an undamped system while symplectic integration almost preserves it the symplectic schemes are extended to ordinary differential equations by means of the lagrangian and hamiltonian and the non linear vibration of beams and plates is studied by the schemes for the first time non linear modal coupling is emphasized the extension to shell structures involves the complication of curvature effects research is in progress

on certain maximal functions and approach regions if f e l ir and u x y is the poisson integral of j a classical theorem of fatou 2 asserts that u has nontangential limits almost everywhere on r littlewood 5 and later zygmund 9 showed that this conclusion is false if nontangential approach is replaced by approach along translates of a curve which approaches the boundary tangentially in this paper we find a necessary and sufficient condition on an approach region for the associated maximal function to be appropriately bounded it then turns out that there are many approach regions which are not contained in any nontangential region but for which the conclusions of fatou s theorem remain true suppose q c ir has the property that whenever xi u e b and whenever x x y y it follows that x v e q then the maximal function associated to such a set is bounded if and only if the cross sectional measure at height y is bounded by a constant times y we also study regions where the cross sectional area is larger than y we introduce a modified maximal function which is again bounded this result leads to a simple proof of the boundedness of certain tangential maximal functions of poisson integrals of potentials studied in 161 the plan of this paper is as follows in section 1 we motivate our main ideas by discussing two particular examples the method of proof here is somewhat different from the proofs of the more general results in section 2 we obtain the necessary and sufficient conditions for fatou s theorem in section 3 we study more general approach regions and the appropriately modified maximal functions in section 4 we show how this maximal function controls the tangential boundary behavior of poisson integrals of potentials

nearly weakly orthonormal sequences singular value estimates and calderon zygmund operators abstract the direct way to estimate the singular values of a compact operator is to decompose it as a sum of orthogonal rank one pieces however such decompositions can generally not be found in practice we give a variation of the decomposition using nearly weakly orthonormal nwo sequences the nwo decomposition is easier to do in examples but is still strong enough to give good singular value estimates we illustrate this by giving sharp trace ideal estimates for the double layer potential and for the first and higher commutators of multiplication operators and calderon zygmund operators in particular nwo sequences seem well suited for dealing with operators which depend nonlinearly on their symbol we also show that the class of operators which admit nwo expansions is well behaved under composition under conjugation by weights and under conjugation by changes of variable

on characterization of poisson integrals of schrodinger operators with bmo traces abstract let l be a schrodinger operator of the form l v acting on l 2 r n where the nonnegative potential v belongs to the reverse holder class b q for some q n let bmo l r n denote the bmo space on r n associated to the schrodinger operator l in this article we will show that a function f bmo l r n is the trace of the solution of l u u t t l u 0 u x 0 f x where u satisfies a carleson condition sup x b r b r b n 0 r b b x b r b t u x t 2 d x d t c conversely this carleson condition characterizes all the l harmonic functions whose traces belong to the space bmo l r n this result extends the analogous characterization founded by fabes johnson and neri in 13 for the classical bmo space of john and nirenberg

an improved symplectic precise integration method for analysis of the rotating rigid flexible coupled system abstract this paper presents an improved symplectic precise integration method pim to increase the accuracy and keep the stability of the computation of the rotating rigid flexible coupled system firstly the generalized hamilton s principle is used to establish a coupled model for the rotating system which is discretized and transferred into hamiltonian systems subsequently secondly a suitable symplectic geometric algorithm is proposed to keep the computational stability of the rotating rigid flexible coupled system thirdly the idea of pim is introduced into the symplectic geometric algorithm to establish a symplectic pim which combines the advantages of the accuracy of the pim and the stability of the symplectic geometric algorithm in some sense the results obtained by this method are analytical solutions in computer for a long span of time so the time step can be enlarged to speed up the computation finally three numerical examples show the stability of computation the accuracy of solving stiff equations and the capability of solving nonlinear equations respectively all these examples prove the symplectic pim is a promising method for the rotating rigid flexible coupled systems

uniformly convex and smooth banach spaces and lp boundedness properties of littlewood paley and area functions associated with semigroups abstract in this paper we obtain new characterizations of the uniformly convex and smooth banach spaces these characterizations are established by using l p boundedness properties of littlewood paley functions and area integrals associated with heat semigroups and involving fractional derivatives our results apply for instance by considering the heat semigroups defined by hermite and laguerre operators that do not satisfy the markovian property

embedding theorems for bergman spaces via harmonic analysis let a p omega denote the bergman space in the unit disc induced by a radial weight omega with the doubling property int r 1 omega s ds le c int frac 1 r 2 1 omega s ds the positive borel measures such that the differentiation operator of order n in mathbb n cup 0 is bounded from a p omega into l q mu are characterized in terms of geometric conditions when 0 p q infty en route to the proof a theory of tent spaces for weighted bergman spaces is built

morphology of growth by random walk deposition we simulate a deposition model with a break of symmetry induced by a point source we 1nd that tsallis anomalous distribution for random walks n x n a 1 b q 1 x 2 q q 1

new orlicz hardy spaces associated with divergence form elliptic operators abstract let l be the divergence form elliptic operator with complex bounded measurable coefficients the positive concave function on 0 of strictly critical lower type p 0 1 and t t 1 1 t 1 for t 0 in this paper the authors study the orlicz hardy space h l r n and its dual space bmo l r n where l denotes the adjoint operator of l in l 2 r n several characterizations of h l r n including the molecular characterization the lusin area function characterization and the maximal function characterization are established the carleson measure characterization and the john nirenberg inequality for the space bmo l r n are also given as applications the authors show that the riesz transform l 1 2 and the littlewood paley g function g l map h l r n continuously into l the authors further show that the riesz transform l 1 2 maps h l r n into the classical orlicz hardy space h r n for p n n 1 1 and the corresponding fractional integral l for certain 0 maps h l r n continuously into h l r n where is determined by and and satisfies the same property as all these results are new even when t t p for all t 0 and p 0 1

tent space well posedness for parabolic cauchy problems with rough coefficients abstract we study the well posedness of cauchy problems on the upper half space r n 1 associated to higher order systems t u 1 m 1 div m a m u with bounded measurable and uniformly elliptic coefficients we address initial data lying in l p 1 p and bmo p spaces and work with weak solutions our main result is the identification of a new well posedness class given for p 1 by distributions satisfying m u t m p 2 where t m p 2 is a parabolic version of the tent space of coifman meyer stein in the range p 2 this holds without any further constraints on the operator and for p it provides a carleson measure characterization of bmo with non autonomous operators we also prove higher order l p well posedness previously only known for the case m 1 the uniform l p boundedness of propagators of energy solutions plays an important role in the well posedness theory and we discover that such bounds hold for p close to 2 this is a consequence of local weak solutions being locally holder continuous with values in spatial l l o c p for some p 2 what is also new for the case m 1

weighted tent spaces with whitney averages factorization interpolation and duality in this paper we introduce a new scale of tent spaces which covers the weighted tent spaces of coifman meyer stein and of hofmann mayboroda mcintosh and some other tent spaces considered by dahlberg kenig pipher and auscher axelsson in studying boundary value problems for elliptic systems the strong factorizations within our tent spaces with applications to quasi banach complex interpolation and to multiplier duality theory are then established this way we unify and extend the corresponding results obtained by coifman meyer stein cohn verbitsky and hytonen rosen

scaling transformation of random walk distributions in a lattice we use a decimation procedure in order to obtain the dynamical renormalization group transformation rgt properties of random walk distribution in a 1 1 lattice we obtain an equation similar to the chapman kolmogorov equation first we show the existence of invariants through the rgt we also show the existence of functions which are semi invariants through the rgt second we show as well that the distribution r q x 1 b q 1 x 2 1 1 q q 1 which is an exact solution of a nonlinear fokker planck equation is a semi invariant for rgt we obtain the map q f q from the rgt and we show that this map has two fixed points q 1 attractor and q 2 repellor which are the gaussian and the lorentzian respectively we show the connections between these result and the levy flights

bmol hn spaces and carleson measures for schrodinger operators abstract let l h n v be a schrodinger operator on the heisenberg group h n where h n is the sub laplacian and the nonnegative potential v belongs to the reverse holder class b q 2 here q is the homogeneous dimension of h n in this article we investigate the dual space of the hardy type space h l 1 h n associated with the schrodinger operator l which is a kind of bmo type space bmo l h n defined by means of a revised sharp function related to the potential v we give the fefferman stein type decomposition of bmo l functions with respect to the adjoint riesz transforms r j l for l and characterize bmo l h n in terms of the carleson measure we also establish the bmo l boundedness of some operators such as the adjoint riesz transforms r j l the littlewood paley function s q l the lusin area integral s q l the hardy littlewood maximal function and the semigroup maximal function all results hold for stratified groups as well

regularity properties of the heat kernel and area integral characterization of hardy space hl1 related to degenerate schrodinger operators abstract in this paper we introduce the area integral associated with the heat semigroup t t t 0 generated by a degenerate schrodinger operator l we obtain a regularity estimate of the kernels of the semigroup t t t 0 this regularity together with a reproducing formula enables us to establish the area integral characterization of the hardy space associated with l

classes of hardy spaces associated with operators duality theorem and applications let l be the infinitesimal generator of an analytic semigroup on l 2 r n with suitable upper bounds on its heat kernels in auscher duong and mcintosh 2005 and duong and yan 2005 a hardy space h1 l r n and a bmo l r n space associated with the operator l were introduced and studied in this paper we define a class of h p l r n spaces associated with the operator l for a range of p 1 acting on certain spaces of morrey campanato functions defined in new morrey campanato spaces associated with operators and applications by duong and yan 2005 and they generalize the classical h p r n spaces we then establish a duality theorem between the h p l r n spaces and the morrey campanato spaces in that same paper as applications we obtain the boundedness of fractional integrals on h p l r n and give the inclusion between the classical h p r n spaces and the h p l r n spaces associated with operators

a new class of function spaces connecting triebel lizorkin spaces and q spaces abstract let s r 0 p 1 and q 1 in this paper we introduce a new class of function spaces f p q s r n which unify and generalize the triebel lizorkin spaces with both p 1 and p and q spaces by establishing the carleson measure characterization of q space we then determine the relationship between triebel lizorkin spaces and q spaces which answers a question posed by dafni and xiao in g dafni j xiao some new tent spaces and duality theorem for fractional carleson measures and q r n j funct anal 208 2004 377 422 moreover via the hausdorff capacity we introduce a new class of tent spaces f t p q s r n 1 and determine their dual spaces f w p q s q r n where s r p q 1 max p q 1 0 q max p q and t denotes the conjugate index of t 1 as an application of this we further introduce certain hardy hausdorff spaces f h p q s r n and prove that the dual space of f h p q s r n is just f p q s q r n when p q 1

conical square functions associated with bessel laguerre and schrodinger operators in umd banach spaces abstract in this paper we consider conical square functions in the bessel laguerre and schrodinger settings where the functions take values in umd banach spaces following a recent paper of hytonen van neerven and portal 36 in order to define our conical square functions we use radonifying operators we obtain new equivalent norms in the lebesgue bochner spaces l p 0 b and l p r n b 1 p in terms of our square functions provided that b is a umd banach space our results can be seen as banach valued versions of known scalar results for square functions

theory and experiments for large amplitude vibrations of rectangular plates with geometric imperfections abstract large amplitude vibrations of rectangular plates subjected to harmonic excitation are investigated the von karman nonlinear strain displacement relationships are used to describe the geometric nonlinearity a specific boundary condition with restrained normal displacement at the plate edges and fully free in plane displacements not previously considered has been introduced as a consequence that it is very close to the experimental boundary condition results for this boundary condition are compared to nonlinear results previously obtained for i simply supported plates with immovable edges ii simply supported plates with movable edges and iii fully clamped plates the nonlinear equations of motion are studied by using a code based on pseudo arclength continuation method a thin rectangular stainless steel plate has been inserted in a metal frame this constraint is approximated with good accuracy by the newly introduced boundary condition the plate inserted into the frame has been measured with a 3d laser system in order to reconstruct the actual geometry and identify geometric imperfections out of planarity the plate has been experimentally tested in laboratory for both the first and second vibration modes for several excitation magnitudes in order to characterize the nonlinearity of the plate with imperfections numerical results are able to follow experimental results with good accuracy for both vibration modes and for different excitation levels once the geometric imperfection is introduced in the model effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are shown convergence of the solution with the number of generalized coordinates is numerically verified

characterization of two weighted inequalities for multilinear fractional maximal operator abstract in this paper we restudied the two weight problem of multilinear fractional maximal operator m first we gave a characterization of two weight inequalities for m related to a multilinear analogue of sawyer s two weight condition s p q which essentially improved and extended some known results before this was done mainly by using the technique of the well known atomic decomposition of tent space then we obtained the strong boundedness of m associated with multiple weight a p q class which removed the power bump condition assumed in the known results before finally a new two weight b p q condition was introduced and the two weight inequality of m with b p q condition was established

a discrete transform and decompositions of distribution spaces abstract we study a representation formula of the form q q q for a distribution on r n this formula is obtained by discretizing and localizing a standard littlewood paley decomposition the map taking to the sequence q q with q running over the dyadic cubes in r n is called the transform the functions q and q have a particularly simple form moreover most of the familiar distribution spaces lp spaces 1 r n we also consider pointwise multipliers for the characteristic function of a domain we obtain boundedness results for a general class of domains which properly includes lipschitz domains several interpolation methods are easily analyzed via the sequence spaces for real interpolation we obtain among other things an extension to the case p 0 this in turn gives a new approach to the traditional atomic decomposition of hardy spaces

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

pointwise multipliers and decomposition theorems in f q s in this paper we give a characterization of the pointwise multipliers of the holomorphic triebel lizorkin spaces f q s and we apply these results to prove a corona decomposition theorem for these spaces

nonlinear curvature based model and resonant finite amplitude vibrations of symmetric cross ply laminates abstract moving from a general plate theory a modified general classical laminated plate theory mgclpt exhibiting nonlinear curvatures but still allowing for some worth features of linear curvature models von karman is formulated starting from mgclpt partial differential equations a minimal discretized model suitable for the analysis of resonant finite amplitude vibrations of symmetric cross ply laminates with immovable or movable supports is obtained via the galerkin procedure periodic responses of a single mode model and of a 3 1 internally resonant two mode model excited at primary resonance are obtained via the multiple time scale method the influence of various system parameters thickness ratio plate aspect number of laminae kind of material mode number is addressed and the comparison of nonlinear vibration results as obtained with the mgclpt and the von karman models for different boundary conditions shows some interesting differences

factorization of tent spaces and hankel operators it is shown that the factorization tpq tp t q for tent spaces proved by r r coifman et al 1985 j funct anal 62 304 335 for p q q 2 holds true for all 0 p q from this certain strong factorization theorems are derived for spaces hps of fractional derivatives of hp functions and more general triebel spaces in particular it is proved that hps hp bmoas applications considered include characterizations of symbols of bounded hankel operators h hp hqs complex interpolation of tent spaces and carleson measure theorems for derivatives of hp functions

quasiconformal mappings and chord arc curves given a quasiconformal mapping p on the plane what conditions on its dilatation guarantee that p r is rectifiable and pir is locally abso lutely continuous we show in this paper that if satisfies certain quadratic carleson measure conditions with small norm then p r is a chord arc curve with small constant and p x p 0 g0 ea t dt for x e r with a e bmo having small norm conversely given any such map from r c we show that it has an extension to c with the right kind of dilatation similar results hold with r replaced by a chord arc curve examples are given that show that it would be hard to improve these results applications are given to conformal welding and the theorem of coifman and meyer on the real analyticity of the riemann mapping on the manifold of chord arc curves let p be a quasiconformal map of the plane onto itself thus p is a homeomorphism with locally integrable distributional derivatives and ps upz where u e l c il ul100 1 here we use the notations fz af azf 2 z id f fz 2 aa ida f this function u is called the complex dilatation of p the mapping theorem for q c maps states that for each u e l c il ul100 1 there is a q c map p on c with dilatation u and p is unique up to normalization a basic problem is to understand how geometric properties of p are reflected in u for example one would like to have natural conditions on u which imply that p r is rectifiable and p ir is absolutely continuous this question arises naturally when considering problems in conformal mappings and conformal welding in this paper we obtain such estimates for the mapping theorem and we also give some applications our results involve bmo aoo weights chord arc curves and carleson measures and so we first review the appropriate definitions a locally integrable function f on r lies in bmo if llfil sup lil if x fil dx received by the editors june 1 1986 1980 mathematics subject classification 1985 revision primary 30g60 secondary 42b20 30e20

abstract capacitary estimates and the completeness and separability of certain classes of non locally convex topological vector spaces abstract we are concerned with establishing completeness and separability criteria for large classes of topological vector spaces which are typically non locally convex including lebesgue like spaces lorentz spaces orlicz spaces mixed normed spaces tent spaces and discrete triebel lizorkin and besov spaces for vector spaces of measurable functions we also derive pointwise convergence results our approach relies on abstract capacitary estimates and works in certain cases of interest even in the absence of a background measure space and or of a vector space structure

harmonic analysis on quantum tori this paper is devoted to the study of harmonic analysis on quantum tori we consider several summation methods on these tori including the square fej r means square and circular poisson means and bochner riesz means we first establish the maximal inequalities for these means then obtain the corresponding pointwise convergence theorems in particular we prove the noncommutative analogue of the classical stein theorem on bochner riesz means the second part of the paper deals with fourier multipliers on quantum tori we prove that the completely bounded l p fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension finally we present the littlewood paley theory associated with the circular poisson semigroup on quantum tori we show that the hardy spaces in this setting possess the usual properties of hardy spaces as one can expect these include the quantum torus analogue of fefferman s h 1 bmo duality theorem and interpolation theorems our analysis is based on the recent developments of noncommutative martingale ergodic inequalities and littlewood paley stein theory

estimates for 8706 μ 1 and calderon s theorem on the cauchy integral etude du caractere borne de l operateur integral de cauchy a l aide d une transformation quasi conforme

conical stochastic maximal l p regularity for 1 leqslant p infty let a mathrm div a cdot nabla be a second order divergence form elliptic operator on mathbb r n with bounded measurable real valued coefficients and let w be a cylindrical brownian motion in a hilbert space h our main result implies that the stochastic convolution process begin aligned u t int 0 t e t s a g s dw s quad t geqslant 0 end aligned satisfies for all 1 leqslant p infty a conical maximal l p regularity estimate begin aligned mathbb e vert nabla u vert t 2 p 2 mathbb r times mathbb r n p leqslant c p p mathbb e vert g vert t 2 p 2 mathbb r times mathbb r n h p end aligned here t 2 p 2 mathbb r times mathbb r n and t 2 p 2 mathbb r times mathbb r n h are the parabolic tent spaces of real valued and h valued functions respectively this contrasts with krylov s maximal l p regularity estimate begin aligned mathbb e vert nabla u vert l p mathbb r l 2 mathbb r n mathbb r n p leqslant c p mathbb e vert g vert l p mathbb r l 2 mathbb r n h p end aligned which is known to hold only for 2 leqslant p infty even when a delta and h mathbb r the proof is based on an l 2 estimate and extrapolation arguments which use the fact that a satisfies suitable off diagonal bounds our results are applied to obtain conical stochastic maximal l p regularity for a class of nonlinear spdes with rough initial data

embedding bergman spaces into tent spaces let a p omega denote the bergman space in the unit disc mathbb d of the complex plane induced by a radial weight omega with the doubling property int r 1 omega s ds le c int frac 1 r 2 1 omega s ds the tent space t q s nu omega consists of functions such that begin aligned begin aligned vert f vert t q s nu omega q int mathbb d left int vargamma zeta f z s d nu z right frac q s omega zeta da zeta infty quad 0 q s infty end aligned end aligned here vargamma zeta is a non tangential approach region with vertex zeta in the punctured unit disc mathbb d setminus 0 we characterize the positive borel measures nu such that a p omega is embedded into the tent space t q s nu omega where 1 frac s p frac s q 0 by considering a generalized area operator the results are provided in terms of carleson measures for a p omega

the qp carleson measure problem let be a nonnegative borel measure on the open unit disk this note shows how to decide that the mobius invariant space covering and is boundedly resp compactly embedded in the quadratic tent type space interestingly the embedding result can be used to determine the boundedness resp compactness of the volterra type and multiplication operators on

product hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type the aim of this article is to develop the theory of product hardy spaces associated with operators which possess the weak assumption of davies gaffney heat kernel estimates in the setting of spaces of homogeneous type we also establish a calderon zygmund decomposition on product spaces which is of independent and use it to study the interpolation of these product hardy spaces we then show that under the assumption of generalized gaussian estimates the product hardy spaces coincide with the lebesgue spaces for an appropriate range of p

a decomposition theorem for bmo and applications abstract every function having bounded mean oscillation bmo on the line is written as a sum of coefficients times normalized rational functions with the coefficients satisfying a carleson measure packing condition this decomposition theorem and related techniques are used to obtain operator norm estimates for first and second order commutators and direct and converse singular value estimates for hankel operators and products of hankel operators

layer potentials and boundary value problems for elliptic equations with complex l coefficients satisfying the small carleson measure norm condition abstract we consider divergence form elliptic equations l u a u 0 in the half space r n 1 x t r n 0 whose coefficient matrix a is complex elliptic bounded and measurable in addition we suppose that a satisfies some additional regularity in the direction transverse to the boundary namely that the discrepancy a x t a x 0 satisfies a carleson measure condition of fefferman kenig pipher type with small carleson norm under these conditions we establish a full range of boundedness results for double and single layer potentials in l p hardy sobolev bmo and holder spaces furthermore we prove solvability of the dirichlet problem for l with data in l p r n bmo r n and c r n and solvability of the neumann and regularity problems with data in the spaces l p r n h p r n and l 1 p r n h 1 p r n respectively with the appropriate restrictions on indices assuming invertibility of layer potentials for the t independent operator l 0 a 0

hardy and bmo spaces associated to divergence form elliptic operators consider a second order divergence form elliptic operator l with complex bounded measurable coefficients in general operators based on l such as the riesz transform or square function may lie beyond the scope of the calderon zygmund theory they need not be bounded in the classical hardy bmo and even some l p spaces in this work we develop a theory of hardy and bmo spaces associated to l which includes in particular a molecular decomposition maximal and square function characterizations duality of hardy and bmo spaces and a john nirenberg inequality

numerical methods for thermally stressed shallow shell equations abstract we develop efficient and accurate numerical methods to solve a class of shallow shell problems of the von karman type the governing equations form a fourth order coupled system of nonlinear biharmonic equations for the transverse deflection and airy s stress function a second order finite difference discretization with three iterative methods picard newton and trust region dogleg is proposed for the numerical solution of the nonlinear pde system three simple boundary conditions and two application motivated mixed boundary conditions are considered along with the nonlinearity of the system boundary singularities that appear when mixed boundary conditions are specified are the main numerical challenges two approaches that use either a transition function or local corrections are developed to deal with these boundary singularities all the proposed numerical methods are validated using carefully designed numerical tests where expected orders of accuracy and rates of convergence are observed a rough run time performance comparison is also conducted to illustrate the efficiency of our methods as an application of the methods a snap through thermal buckling problem is considered the critical thermal loads of shell buckling with various boundary conditions are numerically calculated and snap through bifurcation curves are also obtained using our numerical methods together with a pseudo arclength continuation method our results are consistent with previous studies

hardy spaces associated with magnetic schrodinger operators on strongly lipschitz domains abstract let p 0 1 be a strongly lipschitz domain in r n and a i a i a v a magnetic schrodinger operator on l 2 satisfying the dirichlet boundary condition where a a 1 a n l loc 2 r n and 0 v l loc 1 in this paper the authors introduce the hardy space h a p by the lusin area function associated with a and establish its equivalent characterization via the non tangential maximal function associated with e t a t 0 as applications the authors obtain the boundedness of the riesz transforms l k a 1 2 k 1 n from h a p to l p for p 0 1 and the fractional integral a from h a p to h a q for 0 p q 1 and n 2 1 p 1 q where l k is the closure of x k i a k in l 2

hardy spaces and divergence operators on strongly lipschitz domains of rn abstract let be a strongly lipschitz domain of r n consider an elliptic second order divergence operator l including a boundary condition on and define a hardy space by imposing the non tangential maximal function of the extension of a function f via the poisson semigroup for l to be in l1 under suitable assumptions on l we identify this maximal hardy space with h 1 r n if r n with h r 1 under the dirichlet boundary condition and with h z 1 under the neumann boundary condition

a note onbmoand bloch space of generalized α β harmonic functions abstract in this paper we study functions in the unit ball in c n annihilated by the differential operators c given by formula we obtain two equivalent carleson measure characterizations of those of such functions having boundary value in bmo we also give analogous carleson bergman measure characterizations of harmonic bloch functions

scaling transformation of random walk and generalized statistics abstract we use a decimation procedure in order to obtain the dynamical renormalization group transformation rgt properties of random walk distribution in a 1 1 lattice we obtain an equation similar to the chapman kolmogorov equation first we show the existence of invariants of the rgt and that the tsallis distribution r q x 1 b q 1 x 2 1 1 q q 1 is a quasi invariant of the rgt we obtain the map q f q from the rgt and show that this map has two fixed points q 1 attractor and q 2 repellor which are the gaussian and the lorentzian respectively finally we use those concepts to show that the nonadditivity of the tsallis entropy needs to be reviewed

imbedding potentials in tent spaces abstract we obtain characterizations of positive borel measures on b n so that the nonisotropic potential space k lp d is imbedded in the tent space t2q d where 1 q we deduce characterizations for pointwise multipliers of the space h p

an energy preserving description of nonlinear beam vibrations in modal coordinates abstract conserved quantities are identified in the equations describing large amplitude free vibrations of beams projected onto their linear normal modes this is achieved by writing the geometrically exact equations of motion in their intrinsic or hamiltonian form before the modal transformation for nonlinear free vibrations about a zero force equilibrium it is shown that the finite dimensional equations of motion in modal coordinates are energy preserving even though they only approximate the total energy of the infinite dimensional system for beams with constant follower forces energy like conserved quantities are also obtained in the finite dimensional equations of motion via casimir functions the duality between space and time variables in the intrinsic description is finally carried over to the definition of a conserved quantity in space which is identified as the local cross sectional power numerical examples are used to illustrate the main results

vmo spaces associated with divergence form elliptic operators consider the second order divergence form elliptic operator l with complex bounded coefficients in this paper we introduce and develop a function space vmol of vanishing mean oscillation associated with the operator l using the theory of tent spaces and the littlewood paley theory we prove that the hardy space h l 1 of hofmann and mayboroda introduced in hofmann and mayboroda math ann 344 37 116 2009 is the dual of our rm vmo l ast in which l is the adjoint operator of l we also give an equivalent characterization of the space vmol in the context of the theory of tent spaces

shear deformable versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates in the present study i the classical von karman theory ii the first order shear deformation theory and iii the higher order third order shear deformation theory are compared for studying the nonlinear forced vibrations of isotropic and laminate composite rectangular plates in particular the harmonic response in the frequency neighborhood of the fundamental mode of rectangular plates is investigated and the response curves computed by using the three different theories are compared the boundary conditions of the plates are simply supported with immovable edges geometric imperfections are taken into account calculations for isotropic and laminated composite plates are presented and results are discussed for isotropic plates the frequency response curves for large amplitude vibrations obtained by using the three theories are almost coincident for laminated composite plates differences arise for relatively thick plates ratio between the thickness and the edge equal to 0 1 while for thin plates ratio between the thickness and the edge equal to 0 01 no difference is obtained for all cases the first order shear deformation with shear correction factor 3 2 and the higher order shear deformation theories give practically coincident results and differences are observed with respect to the classical von karman theory

weighted maximal regularity estimates and solvability of non smooth elliptic systems i we develop new solvability methods for divergence form second order real and complex elliptic systems above lipschitz graphs with l 2 boundary data the coefficients a may depend on all

tent space boundedness via extrapolation we study the action of operators on tent spaces such as maximal operators calderon zygmund operators riesz potentials we also consider singular non integral operators we obtain boundedness as an application of extrapolation methods in the banach range in the non banach range boundedness results for calderon zygmund operators follow by using an appropriate atomic theory we end with some consequences on amalgam spaces

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

the atomic decomposition of weighted hardy spaces associated to self adjoint operators on product spaces abstract let l be a non negative self adjoint operator acting on l 2 r n satisfying a pointwise gaussian estimate for its heat kernel let w be an a p weight on r n r n 1 p in this article we obtain a weighted q atomic decomposition with q p for the weighted hardy space h l w 1 r n r n associated to l

the regularity problem for second order elliptic operators with complex valued bounded measurable coefficients the present paper establishes a certain duality between the dirichlet and regularity problems for elliptic operators with t independent complex bounded measurable coefficients t being the transversal direction to the boundary to be precise we show that the dirichlet boundary value problem is solvable in l p subject to the square function and non tangential maximal function estimates if and only if the corresponding regularity problem is solvable in l p moreover the solutions admit layer potential representations in particular we prove that for any elliptic operator with t independent real possibly non symmetric coefficients there exists a p 1 such that the regularity problem is well posed in l p

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

maximal function characterizations of variable hardy spaces associated with non negative self adjoint operators satisfying gaussian estimates abstract let p r n 0 1 be a variable exponent function satisfying the globally log holder continuous condition and l a non negative self adjoint operator on l 2 r n whose heat kernels satisfying the gaussian upper bound estimates let h l p r n be the variable exponent hardy space defined via the lusin area function associated with the heat kernels e t 2 l t 0 in this article the authors first establish the atomic characterization of h l p r n using this the authors then obtain its non tangential maximal function characterization which when p is a constant in 0 1 coincides with a recent result by l song and l yan 2016 and further induces the radial maximal function characterization of h l p r n under an additional assumption that the heat kernels of l have the holder regularity