gaussian heat kernel upper bounds via the phragmen lindelof theorem we prove that in presence of l gaussian estimates so called davies gaffney estimates on diagonal upper bounds imply precise off diagonal gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces

semigroup kernels poisson bounds and holomorphic functional calculus letlbe the generator of a continuous holomorphic semigroupswhose action is determined by an integral kernelkon a scale of spaceslp x under mild geometric assumptions on x we prove that iflhas a boundedh functional calculus onl2 x andksatisfies bounds typical for the poisson kernel thenlhas a boundedh functional calculus onlp x for eachp 1 moreover if x is of polynomial type andksatisfies second order gaussian bounds we establish criteria forlto have a bounded hormander functional calculus or a bounded davies helffer sjostrand functional calculus

cubic structures equivariant euler characteristics and lattices of modular forms we use the theory of cubic structures to give a fixed point riemann roch formula for the equivariant euler characteristics of coherent sheaves on projective at schemes over z with a tame action of a finite abelian group this formula supports a conjecture concerning the extent to which such equivariant euler characteristics may be determined from the restriction of the sheaf to an infinitesimal neighborhood of the fixed point locus our results are applied to study the module structure of modular forms having fourier coeficients in a ring of algebraic integers as well as the action of diamond hecke operators on the mordell weil groups and tate shafarevich groups of jacobians of modular curves

maximal parabolic regularity for divergence operators including mixed boundary conditions abstract we show that elliptic second order operators a of divergence type fulfill maximal parabolic regularity on distribution spaces even if the underlying domain is highly non smooth the coefficients of a are discontinuous and a is complemented with mixed boundary conditions applications to quasilinear parabolic equations with non smooth data are presented

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

weighted norm inequalities gaussian bounds and sharp spectral multipliers abstract let l be a non negative self adjoint operator acting on l 2 x where x is a space of homogeneous type assume that l generates a holomorphic semigroup e t l whose kernels p t x y have gaussian upper bounds but there is no assumption on the regularity in variables x and y in this article we study weighted l p norm inequalities for spectral multipliers of l we show that sharp weighted hormander type spectral multiplier theorems follow from gaussian heat kernel bounds and appropriate l 2 estimates of the kernels of the spectral multipliers these results are applicable to spectral multipliers for large classes of operators including laplace operators acting on lie groups of polynomial growth or irregular non doubling domains of euclidean spaces elliptic operators on compact manifolds and schrodinger operators with non negative potentials

a spectral multiplier theorem for non self adjoint operators we prove a spectral multiplier theorem for non self adjoint operators more precisely we consider non self adjoint operators a d a c l 2 l 2 having numerical range in a sector w of angle w and whose heat kernel satisfies a gaussian upper bound we prove that for every bounded holomorphic function f on w f a acts on l p with l p norm estimated by the behavior of a finite number of derivatives of f on the boundary of w

on the littlewood paley stein g function we consider semigroups tt which are contractive on lp m for all p e q q and q e 1 2 we give an example on symmetric spaces of the noncompact type which shows that the littlewood paley stein g function associated to the infinitesimal generator of tt may be unbounded on lq m and on l m we prove that variants of the g function are bounded on these lebesgue spaces in this paper we present some new results concerning the lp boundedness of the littlewood paley stein g function suppose that tt is a co semigroup of operators on lp m where m is a a finite measure space and let a e n the littlewood paley stein function ga associated to the given semigroup is defined by the rule ga f 1 ta ttfi2 dt for all f for which the right hand side makes sense in classical cases where tt is the poisson semigroup acting on lp r or lp t the g function is an important tool in fourier analysis for instance it is frequently used to prove multiplier theorems and pointwise convergence results the reader is referred to 1 1 for a survey of its role in a general context the g function was considered by e m stein he proved that if tt is a symmetric diffusion semigroup then ga satisfies the estimate 1 aplifiip liga f iip bp fllp vf e lp m whenever p e 1 oo a proof of this result can be found in 10 a simpler and more general approach via transference techniques is presented in 2 a third proof is in 4 and 5 it is of an entirely different nature in that it is based on the fact that generators of symmetric diffusion semigroups and even more general semigroups 3 have an hx functional calculus one of the interesting applications of g functions is to functional calculus for infinitesimal generators of co semigroups stein proved a marcinkiewicz type result for those as a corollary of the theory he developed for the g function the relationship between g functions and functional calculus for the infinitesimal generator of tt was investigated in 4 and 5 our treatment here owes received by the editors march 7 1994 originally communiated to the proceedings of the ams by j marshall ash 1991 mathematics subject classification primary 42b25 47a60 secondary 43a85

optimal l p l q estimates for parabolic boundary value problems with inhomogeneous data in this paper we investigate vector valued parabolic initial boundary value problems mathcal a t x d mathcal b j t x d subject to general boundary conditions in domains g in mathbb r n with compact c 2m boundary the top order coefficients of mathcal a are assumed to be continuous we characterize optimal l p l q regularity for the solution of such problems in terms of the data we also prove that the normal ellipticity condition on mathcal a and the lopatinskii shapiro condition on mathcal a mathcal b 1 dots mathcal b m are necessary for these l p l q estimates as a byproduct of the techniques being introduced we obtain new trace and extension results for sobolev spaces of mixed order and a characterization of triebel lizorkin spaces by boundary data

continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations abstract we prove convergence of the solutions x n of semilinear stochastic evolution equations on a banach space b driven by a cylindrical brownian motion in a hilbert space h d x n t a n x t f n t x n t d t g n t x n t d w h t x n 0 n assuming that the operators a n converge to a and the locally lipschitz functions f n and g n converge to the locally lipschitz functions f and g in an appropriate sense moreover we obtain estimates for the lifetime of the solution x of the limiting problem in terms of the lifetimes of the approximating solutions x n we apply the results to prove global existence for reaction diffusion equations with multiplicative noise and a polynomially bounded reaction term satisfying suitable dissipativity conditions the operator governing the linear part of the equation can be an arbitrary uniformly elliptic second order elliptic operator

a t 1 theorem for non integral operators let x be a space of homogeneous type and let l be a sectorial operator with bounded holomorphic functional calculus on l 2 x we assume that the semigroup e tl t 0 satisfies davies gaffney estimates associated with l are certain approximations of the identity we call an operator t a non integral operator if compositions involving t and these approximations satisfy certain weighted norm estimates the davies gaffney and the weighted norm estimates are together a substitute for the usual kernel estimates on t in calderon zygmund theory in this paper we show under the additional assumption that a vertical littlewood paley stein square function associated with l is bounded on l 2 x that a non integral operator t is bounded on l 2 x if and only if t 1 in bmo l x and t 1 in bmo l x here bmo l x and bmo l x denote the recently defined bmo x spaces associated with l that generalize the space bmo x of john and nirenberg generalizing a recent result due to f bernicot we show a second version of a t 1 theorem under weaker off diagonal estimates which gives a positive answer to a question raised by him as an application we prove l 2 x boundedness of a paraproduct operator associated with l we moreover study criterions for a t b theorem to be valid

what is not in the domain of the laplacian on sierpinski gasket type fractals abstract we consider the analog of the laplacian on the sierpinski gasket and related fractals constructed by kigami a function f is said to belong to the domain of if f is continuous and f is defined as a continuous function we show that if f is a nonconstant function in the domain of then f2 is not in the domain of we give two proofs of this fact the first is based on the analog of the pointwise identity f2 2f f f 2 where we show that f 2 does not exist as a continuous function in fact the correct interpretation of f2 is as a singular measure a result due to kusuoka we give a new proof of this fact the second is based on a dichotomy for the local behavior of a function in the domain of at a junction point x0 of the fractal in the typical case nonvanishing of the normal derivative we have upper and lower bounds for f x f x0 in terms of d x x0 for a certain value and in the nontypical case vanishing normal derivative we have an upper bound with an exponent greater than 2 this method allows us to show that general nonlinear functions do not operate on the domain of

maximal inequalities and riesz transform estimates on lp spaces for magnetic schrodinger operators ii the paper concerns the magnetic schrodinger operator h bf a v sum j 1 n frac 1 i frac partial partial x j a j 2 v on mathbb r n we prove some lp estimates on the riesz transforms of h and we establish some related maximal inequalities the conditions that we arrive at are essentially based on the control of the magnetic field by the electric potential

hardy littlewood theory for semigroups soit t t t 0 un semi groupe symetrique sousmarkovien et soit n 2 alors on a les proprietes equivalentes a dim t t n b il existe c 2 0 s t t t f c 2 t n 2 f 1 f l 1 x t 0 en fait a b meme dans le cas n 2

some results about complex powers of closed operators the aim of this paper is to give some further results about complex powers of operators a tool that the authors already employed in 2 and s to study some questions of operator theory our first result is essentially a completion of corollary 2 9 of 2 since it gives an estimate for the rate of decrease of a a at infinity when a is a positive operator with bounded imaginary powers we remark that the converse question i e the estimate of the imaginary powers in terms of the amplitude of the spectrum remains open next we prove a result of pertubation if we add to a positive operator

riesz transforms in the absence of a preservation condition with applications to the dirichlet laplacian abstract let l be a linear operator defined such that l generates an associated heat semigroup e t l suppose this semigroup does not satisfy a preservation condition a proof that a generalised riesz transform d g l satisfies l p bounds for some range 2 p q is provided based on two new estimates one is a hardy type inequality for l the other a bound regarding how the gradient of the heat semigroup acts on a characteristic function applications are to cases where l is the dirichlet laplacian on inner uniform subsets of r n

new thoughts on old results of r t seeley in this paper we show that the lp realization of a vector valued elliptic boundary value problem j admits a bounded calculus on lp g e 1 p provided the top order coefficients of are holder continuous here g denotes a domain in n with compact c2m boundary and e a banach space of class our proof is based on an abstract perturbation result for operators admitting bounded calculus and kernel estimates for the solution of j

weighted norm inequalities off diagonal estimates and elliptic operators part i general operator theory and weights this is the first part of a series of four articles in this work we are interested in weighted norm estimates we put the emphasis on two results of different nature one is based on a good inequality with two parameters and the other uses calderon zygmund decomposition these results apply well to singular non integral operators and their commutators with bounded mean oscillation functions singular means that they are of order 0 non integral that they do not have an integral representation by a kernel with size estimates even rough so that they may not be bounded on all lp spaces for 1 p 8 pointwise estimates are then replaced by appropriate localized lp lq estimates we obtain weighted lp estimates for a range of p that is different from 1 8 and isolate the right class of weights in particular we prove an extrapolation theorem a la rubio de francia for such a class and thus vector valued estimates

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

ultracontractivity and the heat kernel for schrodinger operators and dirichlet laplacians abstract abstract connections between integral kernels of positivity preserving semigroups and suitable lp contractivity properties are established then these questions are studied for the semigroups generated by v and h the dirichlet laplacian for an open connected region as an application under a suitable hypothesis sobolev estimates are proved valid up to of the form x c 0 x h k 2 where 0 is the unique positive l2 eigenfunction of h

maximal inequalities and riesz transform estimates on lp spaces for magnetic schrodinger operators i the paper concerns the magnetic schrodinger operator h a v j 1n 1i xj aj 2 v on rn under certain conditions given in terms of the reverse holder inequality on the magnetic field and the electric potential we prove some lp estimates on the riesz transforms of h and we establish some related maximal inequalities

equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form we study the heat kernel of higher order elliptic operators or systems under divergence form on rn ellipticity is in the sense of garding inequality we show that for homogeneous operators gaussian upper bounds and holder regularity of the heat kernel is equivalent to local regularity of weak solutions we also show stability of such bounds under l perturbations of the coefficients or under perturbations with bounded coefficients lower order terms such a criterion allows us to obtain heat kernel bounds for operators or systems with uniformly continuous or vmo coefficients

on a polynomial scalar perturbation of a schrodinger system in lp spaces abstract in the paper 10 the l p realization l p of the matrix schrodinger operator l u d i v q u v u was studied the generation of a semigroup in l p r d c m and characterization of the domain d l p has been established in this paper we perturb the operator l p by a scalar potential belonging to a class including all polynomials and show that still we have a strongly continuous semigroup on l p r d c m with domain embedded in w 2 p r d c m we also study the analyticity compactness positivity and ultracontractivity of the semigroup and prove gaussian kernel estimates further kernel estimates and asymptotic behaviour of eigenvalues of the matrix schrodinger operator are investigated

reduced heat kernels on nilpotent lie groups letu be a basis representation of an irreducible unitary representation of a nilpotent lie groupg inl2 rk and letdu denote the representation of the lie algebrag obtained by differentiation ifb1 b d is a basis ofg andb i du b i we consider the operators h sum limits i j 1 d c ij b i b j sum limits i 1 d c i b i wherec c ij is a real symmetric strictly positive matrix andc i c thenh generates a continuous semigroups holomorphic in the open right half plane with a reduced kernek defined by s z varphi x int limits r k dy kappa z x y varphi y we prove gaussian off diagonal bounds and exponential on diagonal bounds for for example ifc i 0 we establish that left kappa t x y right leqq a 1 wedge varepsilon mu t k mathord left vphantom k 2 right kern nulldelimiterspace 2 e lambda 1 t e d x y 2 4 1 varepsilon t 1 for allt 0 and 0 1 where is the smallest eigenvalue ofc 1 is the smallest eigenvalue ofh andd is a natural distance associated with the coefficientsc and the representationu bounds are also obtained forc i and complext alternatively ifh is self adjoint then left kappa z x y right leqq ae lambda 1 operatorname re z e b left x right alpha left y right alpha for allz c with rez 1 for some 0 2

kernel and eigenfunction estimates for some second order elliptic operators abstract for a potential v such that v x x with 2 we prove that the heat kernel k t x y associated to the uniformly elliptic operator a j k 1 n k a j k j v satisfies the estimate k t x y c e 0 t e c t b e 2 2 x 1 2 x 4 n 1 2 e 2 2 y 1 2 y 4 n 1 2 for large x y r n and all t 0 here 0 1 is an appropriate constant b 2 2 and 0 is the first eigenvalue of a we also obtain an estimate for large x of the eigenfunctions of a

on second order periodic elliptic operators in divergence form we consider second order strongly elliptic operators with complex coecients in divergence form on r d we assume that the coecients are all periodic with a common period if the coecients are continu ous we derive gaussian bounds with the correct small and large time asymptotic behaviour on the heat kernel and all its holder deriva tives moreover we show that the first order riesz transforms are bounded on the lp spaces with p 2 h1 1i secondly if the coe cients are holder continuous we prove that the first order derivatives of the kernel satisfy good gaussian bounds then we establish that the second order derivatives exist and satisfy good bounds if and only if the coecients are divergence free or if and only if the second order riesz transforms are bounded finally if the third order derivatives exist with good bounds then the coecients must be constant

small data scattering of semirelativistic hartree equation abstract in this paper we study the small data scattering of hartree type semirelativistic equation in space dimension 3 the hartree type nonlinearity is v u 2 u and the potential v which generalizes the yukawa has some growth condition we show that the solution scatters to linear solution if an initial data given in h s 1 is sufficiently small and s 1 4 here h s 1 is sobolev type space taking in angular regularity with norm defined by h s 1 h s s h s to establish the results we employ the recently developed strichartz estimate which is l 2 averaged on the unit sphere s 2 and construct the resolution space based on u p v p space

the kalton lancien theorem revisited maximal regularity does not extrapolate abstract we give a new more explicit proof of a result by kalton and lancien stating that on each banach space with an unconditional basis not isomorphic to a hilbert space there exists a generator a of a holomorphic semigroup which does not have maximal regularity in particular we show that there always exists a schauder basis f m such that a can be chosen of the form a m 1 a m f m m 1 2 m a m f m moreover we show that maximal regularity does not extrapolate we construct consistent holomorphic semigroups t p t t 0 on l p r for p 1 which have maximal regularity if and only if p 2 these assertions were both open problems our approach is completely different than the one of kalton and lancien we use the characterization of maximal regularity by r sectoriality for our construction

riesz transform gaussian bounds and the method of wave equation for an abstract self adjoint operator l and a local operator a we study the boundedness of the riesz transform al on lp for some 0 a very simple proof of the obtained result is based on the finite speed propagation property for the solution of the corresponding wave equation we also discuss the relation between the gaussian bounds and the finite speed propagation property using the wave equation methods we obtain a new natural form of the gaussian bounds for the heat kernels for a large class of the generating operators we describe a surprisingly elementary proof of the finite speed propagation property in a more general setting than it is usually considered in the literature

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

random weighted sobolev inequalities and application to quantum ergodicity this paper is a continuation of poiret et al ann henri poincare 16 651 689 2015 where we studied a randomisation method based on the laplacian with harmonic potential here we extend our previous results to the case of any polynomial and confining potential v on mathbb r d we construct measures under concentration type assumptions on the support of which we prove optimal weighted sobolev estimates on mathbb r d this construction relies on accurate estimates on the spectral function in a non compact configuration space then we prove random quantum ergodicity results without specific assumption on the classical dynamics finally we prove that almost all bases of hermite functions are quantum uniquely ergodic

discrete maximal l p regularity for finite element operators let a h h 0 be a family of elliptic finite element operators let i 0 t and consider the problem u h t a hu h t f h t t in i u h 0 0 in this paper we show that for 1 0 is said to have discrete maximal l p regularity

analysis of the heat kernel of the dirichlet to neumann operator abstract we prove poisson upper bounds for the kernel k t t 0 of the semigroup generated by the dirichlet to neumann operator if the underlying domain is bounded and has a c boundary we also prove poisson bounds for k z for all z in the right half plane and for all its derivatives

heat semigroup and singular pdes we provide in this work a semigroup approach to the study of singular pdes in the line of the paracontrolled approach developed recently by gubinelli imkeller and perkowski starting from a heat semigroup we develop a functional calculus and introduce a paraproduct based on the semigroup for which commutator estimates and schauder estimates are proved together with their paracontrolled extensions this machinery allows us to investigate singular pdes in potentially unbounded riemannian manifolds under mild geometric conditions as an illustration we study the generalized parabolic anderson model equation and prove under mild geometric conditions its well posed character in small time on a potentially unbounded 2 dimensional riemannian manifold for an equation driven by a coloured noise and for all times for the linear parabolic anderson model equation in 2 dimensional unbounded manifolds this machinery can be extended to an even more singular setting and deal with sobolev spaces rather than holder spaces

riesz transforms and lie groups of polynomial growth abstract let g be a lie group of polynomial growth we prove that the second order riesz transforms on l 2 g dg are bounded if and only if the group is a direct product of a compact group and a nilpotent group in which case the transforms of all orders are bounded

dispersion of small amplitude solutions of the generalized korteweg de vries equation abstract we study the long time behavior of small solutions of the initial value problem for the generalized korteweg de vries equation t u x 3 u x f u 0 gkdv u x 0 g x for the case where f w w s with s 1 4 23 57 3 8625 our results imply that if g l11 g l22 is sufficiently small then sup r 1 t 1 3 u t l in particular the solution tends to zero in the supremum norm the proofs make use of duhamel s formula and dispersion estimates for the linear propagator as well as chain and leibniz rules for fractional derivatives of compositions d f u lp and products d fg lp 0

y system and β deformed n 4 super yang mills we show how the perturbation theory results recently obtained by f fiamberti a santambrogio c sieg and d zanon for operator anomalous dimensions of deformed super yang mills theory can be reproduced from the ads5 cft4 y system proposed by ng v kazakov and p vieira to do this we obtain the general twisted asymptotic solution of this y system of functional equations we show that existence of an additional parameter in the deformed theory allows us to extract rich information about the perturbation theory integrals directly from the y system using this method we found a simple generating function for a broad class of such integrals

heat kernels of second order complex elliptic operators and applications we study the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on rn we obtain gaussian bounds without further assumption ifn 2 and when the principal part has holder continuous coefficients ifn 3 a thorough study of the boundedness properties of the green operator is made in dimension 1 we construct the fundamental solution of these operators in dimension 2 boundedness results of the maximal accretive square roots onlpsobolev spaces and holder spaces are obtained whenn 2 under holder continuity assumption on the coefficients boundedh functional calculi onlp 1 p are also discussed

analysis on lie groups theorie locale diffusion de la chaleur sur des groupes de lie connexes la theorie globale les inegalites de sobolev bases graduees sur des corps lisses construction des bases graduees estimation locale du noyau diffusion de la chaleur demonstration de l inegalite de sobolev locale formes de dirichlet sur des groupes le semi groupe de convolution les conditions de sobolev modifiees

real interpolation of domains of sectorial operators on lp spaces abstract let a be a sectorial operator on a non atomic l p space 1 p whose resolvent consists of integral operators or more generally has a diffuse representation then the fractional domain spaces d a for 0 1 do not coincide with the real interpolation spaces of l q d a as a consequence we obtain that no such operator a has a bounded h calculus if p 1

sobolev algebras on lie groups and riemannian manifolds we prove that on any connected unimodular lie group g the space l p g l g where l p g is the sobolev space of order 0 associated with a sublaplacian is an algebra under pointwise product this generalizes results due to strichartz in the euclidean case to bohnke in the case of stratified groups and others a global version of this fact holds for groups with polynomial growth we give similar results for riemannian manifolds with ricci curvature bounded from below respectively nonnegative

global l p estimates for degenerate ornstein uhlenbeck operators we consider a class of degenerate ornstein uhlenbeck operators in mathbb r n of the kind mathcal a equiv sum i j 1 p 0 a ij partial x i x j 2 sum i j 1 n b ij x i partial x j where aij bij are constant matrices aij is symmetric positive definite on mathbb r p 0 p0 n and bij is such that mathcal a is hypoelliptic for this class of operators we prove global lp estimates 1 p of the kind left vert partial x i x j 2 u right vert l p left mathbb r n right leq c left left vert mathcal a u right vert l p left mathbb r n right left vert u right vert l p left mathbb r n right right rm for i j 1 2 ldots p 0 and corresponding weak type 1 1 estimates this result seems to be the first case of global estimates in lebesgue lp spaces for complete hormander s operators sum x i 2 x 0 proved in absence of a structure of homogeneous group we obtain the previous estimates as a byproduct of the following one which is of interest in its own left vert partial x i x j 2 u right vert l p left s right leq c left vert lu right vert l p left s right for any u in c 0 infty left s right where s is the strip mathbb r n times left 1 1 right and l is the kolmogorov fokker planck operator mathcal a partial t to get this estimate we use in a crucial way the left invariance of l with respect to a lie group structure in mathbb r n 1 and some results on singular integrals on nonhomogeneous spaces recently proved in bramanti revista matematica iberoamericana 2009 in press

analyticity and discrete maximal regularity on lp spaces abstract in the first part of this paper we give the following interpolation result on the analyticity i e the property t i tn c n for all n n of an operator t on lp if t is powerbounded on lp and lq as well as analytic on lp then t is powerbounded and analytic on lr for all r strictly between p and q this is a discrete analogue of the well known corresponding result for analytic semigroups eta as recently shown by the author the analyticity of t is a necessary condition for the maximal regularity of the discrete time evolution equation un 1 tun fn for all n z u0 0 in the second part of this paper we establish the following two sufficient conditions for its maximal regularity t is a subpositive analytic contraction or t is an integral operator satisfying certain poisson bounds these results are discrete analogues of the corresponding results for the maximal regularity of the evolution equation u t au t f t for all t r u 0 0 due to lamberton weis coulhon and duong and hieber and pruss for the poisson bound result of coulhon and duong and hieber and pruss we give a slight improvement and a short proof

plancherel type estimates and sharp spectral multipliers abstract we study general spectral multiplier theorems for self adjoint positive definite operators on l2 x where x is any open subset of a space of homogeneous type we show that the sharp hormander type spectral multiplier theorems follow from the appropriate estimates of the l2 norm of the kernel of spectral multipliers and the gaussian bounds for the corresponding heat kernel the sharp hormander type spectral multiplier theorems are motivated and connected with sharp estimates for the critical exponent for the riesz means summability which we also study here we discuss several examples which include sharp spectral multiplier theorems for a class of scattering operators on r3 and new spectral multiplier theorems for the laguerre and hermite expansions

formes de dirichlet generales et densite des variables aleatoires reelles sur l espace de wiener abstract it is shown that the main properties of dirichlet spaces can be proved without the classical local compacity hypothesis to this purely measurable framework we extend the functional calculus and the energy image density property these results are then applied to the ornstein uhlenbeck semi group on wiener space where it is obtained that the real random variables which are solutions of lipschitzian stochastic differential equations always have probability densities after perhaps an initial deterministic phase

on the galois structure of equivariant line bundles on curves let it be a finite field and let x be a smooth protective curve over k with structure sheaf o let g be a finite group and write cl 0 g for the reduced grothendieck group of the category of g vector bundles in this paper we describe explicitly the subgroup of cl 0 g which is generated by the classes arising from g stable invertible sheaves on tame galois covers of x which have galois group g introduction let k be a finite field of characteristic p9 and let g be a finite abelian group suppose that y x is a tamely ramified galois covering of smooth projective curves over k with galois group g we shall refer to such coverings as tame g covers of x in this paper we study the structure of g stable line bundles on such curves y in order to be more precise we let cl ox g 9 respectively cl k g 9 denote the reduced grothendieck group of x g vector bundles respectively of finitely generated fc g modules which are cohomologically trivial for g suppose that a is a g stable line bundle on y then 4 is an ox g vector bundle and it gives rise to a class f a g c ox g we shall say that an element of c1 0x g is realizable if it may be obtained in this manner for some choice of y and a we shall combine techniques of c m and bu to obtain an explicit description of the subgroup 9 x g of cl ox g which is generated by the subset of realizable classes in conjunction with a riemann roch theorem these results are sufficient to describe explicitly those elements of c k g which arise as the image of the vector bundles a under the refined euler poincare characteristic

non conformality of gamma _ i deformed 4 sym theory we show that the i deformation which was proposed as candidate gauge theory for a non supersymmetric three parameter deformation of the anti de sitter conformal field theory correspondence is not conformally invariant due to a running double trace coupling not even in the t hooft limit moreover this non conformality cannot be cured when we extend the theory by adding at tree level arbitrary multi trace couplings that obey certain minimal consistency requirements our findings suggest a possible connection between this breakdown of conformal invariance and a puzzling divergence recently encountered in the integrability based descriptions of two loop finite size corrections for the single trace operator of two identical chiral fields we propose a test to clarify this

on diagonal estimates on schrodinger semigroup kernels and reduced heat kernels we prove various estimates for the kernels of semigroups generated by schrodinger operators with magnetic field and potential of polynomial growth we also investigate the reduced heat kernels

l p maximal regularity for second order cauchy problems we introduce the concept of l p maximal regularity for second order cauchy problems we prove l p maximal regularity for an abstract model problem and we apply the abstract results to prove existence uniqueness and regularity of solutions for nonlinear wave equations

new function spaces of bmo type the john nirenberg inequality interpolation and applications in this paper we introduce and develop some new function spaces of bmo bounded mean oscillation type on spaces of homogeneous type or measurable subsets of spaces of homogeneous type the new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity and they generalize the classical bmo space we show that the john nirenberg inequality holds on these spaces and they interpolate with lp spaces by the complex interpolation method we then give applications on lp boundedness of singular integrals whose kernels do not satisfy the hormander condition 2005 wiley periodicals inc

exact smoothing properties of schrodinger semigroups we study schrodinger semigroups in the scale of sobolev spaces and show that for kato class potentials the range of such semigroups in lp has exactly two more derivatives than the potential this proves a conjecture of b simon we show that eigenfunctions of schrodinger operators are generically smoother by exactly two derivatives in given sobolev spaces than their potentials we give applications to the relation between the potential s smoothness and particle kinetic energy in the context of quantum mechanics and characterize kinetic energies in coulomb systems the techniques of proof involve leibniz and chain rules for fractional derivatives which are of independent interest as well as a new characterization of the kato class 1 introduction in this paper we attempt a precise study of the action of schrodinger semigroups in the scale of sobolev spaces work in this area was begun by b simon si4 in 1985 he proved a number of positive and negative results on such smoothing and also presented an open question in the form of a conjecture regarding necessary and sufficient conditions on the potential v for smoothing of order s by the semigroup of functions in l2 rd study of schrodinger semigroups is of interest for a number of reasons see

magnon dispersion to four loops in the abjm and abj models the abjm model is a superconformal chern simons theory with supersymmetry which is believed to be integrable in the planar limit however there is a coupling dependent function that appears in the magnon dispersion relation and the asymptotic bethe ansatz that is only known to leading order at strong and weak coupling we compute this function to four loops in perturbation theory by an explicit feynman diagram calculation for both the abjm model and the abj extension the abjm four loop correction has mixed transcendentality while the abj extension adds a term to the abjm correction with highest transcendentality we then compute the four loop wrapping correction for a scalar operator in the 20 representation of su 4 and find that it agrees with a recent prediction of the abjm y system by gromov kazakov and vieira we also propose a limit of the abj model that might be perturbatively integrable at all loop orders but has a short range hamiltonian

riesz transforms on a solvable lie group of polynomial growth we study riesz transforms associated with a sublaplacian h on a solvable lie group g where g has polynomial volume growth it is known that the standard second order riesz transforms corresponding to h are generally unbounded in lp g in this paper we establish boundedness in lp for modified second order riesz transforms which are defined using derivatives on a nilpotent group gn associated with g our method utilizes a new algebraic approach which associates a distinguished choice of cartan subalgebra with the sublaplacian h we also obtain estimates for higher derivatives of the heat kernel of h and give a new proof without the use of homogenization theory of the boundedness of first order riesz transforms our results can be generalized to an arbitrary possibly non solvable lie group of polynomial growth

bounded h infty calculus for a class of nonlocal operators the bidomain operator in the l_q setting the bidomain operator mathbb a a nonlocal operator is studied in a bounded domain omega subset mathbb r d with boundary partial omega of class c 2 within the l q setting for 1 q infty assuming a fairly general framework it is shown that this operator is sectorial invertible on functions with mean zero and admits a bounded h infty calculus with h infty angle 0 in particular it has the property of maximal l p l q regularity and the fractional power domains mathcal d mathbb a alpha are identified furthermore it is shown that mathbb a generates a strongly continuous compact analytic and exponentially stable semigroup on l q 0 omega with q independent purely countable point spectrum sigma mathbb a

algebres de sobolev sur certains groupes nilpotents soit n un groupe de lie nilpotent stratifie on demontre que les espaces de sobolev non isotropes s p sont des algebres de banach pour le produit ordinaire des fonctions lorsque p 1 p ou designe la dimension homogene de n on donne du point de vue de l analyse harmonique dans ces algebres un resultat de synthese spectrale