maximal and minimal representations of gapped and non gapped motifs of a string the problems of finding maximal and minimal equivalent representations for gapped and non gapped motifs as well as finding motifs that characterize a fixed set of occurrence locations for a given string are studied we apply two equivalence relations on representations the first one is the well known occurrence equivalence of motifs the second equivalence is introduced for patterns of occurrence locations to characterize such patterns by motifs for both equivalences quadratic time algorithms are given for finding a maximal representative of an equivalence class finding a minimal representative is shown to be np complete in both cases for non gapped motifs suffix tree based linear time algorithms are given for finding maximal and minimal representatives maximal minimal gapped motifs are composed of blocks that are maximal minimal non gapped motifs maximal and minimal non gapped motifs thus making up a small basis for all motifs the implied bound on the number of gapped motifs that have a fixed number of non gapped blocks is also given

longest repeats with a block of k don t cares a k repeat is a string wk u k v that matches more than one substring of x where is the don t care letter and k 0 we propose an o n log n time algorithm for computing all longest k repeats in a given string x x 1 n the proposed algorithm uses suffix trees to fulfill this task and relies on the ability to answer lowest common ancestor queries in constant time

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

chord arc surfaces with small constant ii good parameterizations abstract in a companion paper we introduced a notion for hypersurfaces in r d 1 that is analogous to the chord arc condition with small constant for planar curves in this paper we address the problem of finding good parameterizations for these surfaces in particular we show that these surfaces must be homeomorphic to r d and we build parameterizations with l p bounds on the gradient and the gradient of the inverse with p as the chord arc constant goes to 0 when d 2 we use the uniformization theorem to find a quasisymmetric parameterization we do not know how to build bilipschitz parameterizations when d 2 or quasisymmetric parameterizations when d 3 the author conjectures that they do not exist in general however we can build bilipschitz reflections in all dimensions and these reflections will satisfy certain extra estimates in terms of carleson measures

on douady earle extension and the contractibility of the vmo teichmuller space abstract douady earle extension provides a quasiconformal extension of a quasisymmetric homeomorphism to the unit disk and induces a continuous self map of beltrami coefficients in this note we show that is also continuous under a stronger topology on those beltrami coefficients which induce vanishing carleson measures and thus project to the vmo teichmuller space an immediate consequence is that the vmo teichmuller space is contractible

on h on the complement of c1 α curves abstract let be a quasiconformal mapping on the plane with complex dilatation we show that if satisfies a certain carleson measure condition then one can transfer h on the upper half plane onto the corresponding space in the complement of the quasicircle r and that this condition on characterizes c 1 curves

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

weil petersson teichmuller space revisited abstract in our previous paper 23 it was proved that a sense preserving homeomorphism g on the unit circle s 1 belongs to the weil petersson class wp s 1 namely g can be extended to a quasiconformal mapping to the unit disk whose beltrami coefficient is square integrable in the poincare metric if and only if g is absolutely continuous such that log g belongs to the sobolev class h 1 2 in this sequel to 23 we show that the smooth hilbert manifold structure on wp s 1 inherited from h 1 2 by the pullback g log g is compatible with the standard hilbert manifold structure introduced by takhtajan teo 27 this enables us to give a fast approach to some results in our previous papers 23 and 24

a poynting vector formulation for thin shells and plates and its application to structural intensity analysis and source localization part i theory this paper deals with a formulation of the poynting vector structural intensity for thin shells and plates and its application to structural intensity analysis and source localization the procedure begins with the insertion of a taylor series expansion of the displacement components about the middle surface of the shell directly into the three dimensional representation of the poynting vector from this representation an average power flow per unit length or equivalently an intensity resultant is derived whose form permits expressibility in terms of force and moment resultants the corresponding equations of continuity for energy are derived for both body and surface forces and the time integral of the net outflow is developed yielding a technique for source localization this technique offers a method for the determination of the structural intensity of thin elastic shells and plates and is successful for source localization

harmonic reflection in quasicircles and well posedness of a riemann hilbert problem on quasidisks abstract a complex harmonic function of finite dirichlet energy on a jordan domain has boundary values in a certain conformally invariant sense by a construction of h osborn we call the set of such boundary values the douglas osborn space one may then attempt to solve the dirichlet problem on the complement for these boundary values this defines a reflection of harmonic functions we show that quasicircles are precisely those jordan curves for which this reflection is defined and bounded we then use a limiting cauchy integral along level curves of green s function to show that the plemelj sokhotski jump formula holds on quasicircles with boundary data in the douglas osborn space this enables us to prove the well posedness of a riemann hilbert problem with boundary data in the douglas osborn space on quasicircles

weil petersson teichmuller space iii dependence of riemann mappings for weil petersson curves the classical riemann mapping theorem implies that there exists a so called riemann mapping which takes the upper half plane onto the left domain bounded by a jordan curve in the extended complex plane the primary purpose of the paper is to study the basic problem how does a riemann mapping depend on the corresponding jordan curve we are mainly concerned with those jordan curves in the weil petersson class namely the corresponding riemann mappings can be quasiconformally extended to the whole plane with beltrami coefficients being square integrable under the poincare metric after giving a geometric characterization of a weil petersson curve we endow the space of all normalized weil petersson curves with a new real hilbert manifold structure in a geometric manner and show that this new structure is topologically equivalent to the standard complex hilbert manifold structure which implies that an appropriately chosen riemann mapping depends continuously on a weil petersson curve and vice versa this can be considered as the first result about the continuous dependence of riemann mappings on non smooth jordan curves

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

chord arc curves and the beurling transform we study the relation between the geometric properties of a quasicircle gamma and the complex dilatation mu of a quasiconformal mapping that maps the real line onto gamma denoting by s the beurling transform we characterize bishop jones quasicircles in terms of the boundedness of the operator i mu s on a particular weighted l 2 space and chord arc curves in terms of its invertibility as an application we recover the l 2 boundedness of the cauchy integral on chord arc curves

on qk teichmuller spaces abstract recently wulan and ye 36 introduced the q k teichmuller spaces and proved some theorems about the theory of q k teichmuller spaces in this note we continue to consider this theory and obtain some results on the q k teichmuller spaces in particular we establish some new characterizations of the little q k teichmuller spaces

does median filtering truly preserve edges better than linear filtering image processing researchers commonly assert that median filtering is better than linear filtering for removing noise in the presence of edges using a straightforward large n decision theory framework this folk theorem is seen to be false in general we show that median filtering and linear filtering have similar asymptotic worst case mean squared error mse when the signal to noise ratio snr is of order 1 which corresponds to the case of constant per pixel noise level in a digital signal to see dramatic benefits of median smoothing in an asymptotic setting the per pixel noise level should tend to zero i e snr should grow very large we show that a two stage median filtering using two very different window widths can dramatically outperform traditional linear and median filtering in settings where the underlying object has edges in this two stage procedure the first pass at a fine scale aims at increasing the snr the second pass at a coarser scale correctly exploits the nonlinearity of the median image processing methods based on nonlinear partial differential equations pdes are often said to improve on linear filtering in the presence of edges such methods seem difficult to analyze rigorously in a decision theoretic framework a popular example is mean curvature motion mcm which is formally a kind of iterated median filtering our results on iterated median filtering suggest that some pde based methods are candidates to rigorously outperform linear filtering in an asymptotic framework

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

l estimates for the bar partial problem in a half planeproblem in a half plane l approche de dualite pour trouver des solutions de f est suffisante pour plusieurs problemes apparaissant en theorie h p on donne des operateurs solution qui permettent de resoudre des problemes non resolubles par la dualite

homogeneous even kernels on surfaces where da y denotes the area measure on the surface extends to a bounded operator on l2 z it follows that if l x is odd homogeneous of degree n and real analytic away from 0 with a good enough radius of convergence on irn i k j oo then the associated opera to r defined as in 2 by using the kernel l gives rise to an l2 bounded opera to r on the surface see se similar results on lipschitz surfaces were established earlier in c m c m and c d m by using the rotation method based on l2 boundedness of the cauchy integral of calder6n along lipshitz curves not ice that the ro ta t ion method can only produce odd kernels it is natural to ask what happens when the kernels of the form 1 are even when ir it was proved that see st sw for example a sufficient condit ion for ta to be l2 ir n bounded is that

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

layer potentials and boundary value problems for elliptic systems in lipschitz domains various layer potential operators are constructed for general elliptic systems of partial differential equations with constant coefficients these operators are used to study the boundary value problems for these systems for a bounded lipschitz domain in rn n 3 it is shown that if the coefficients of the system satisfy the legendre hadamard condition and a symmetry condition then there exists a unique solution u of the system that solves the dirichlet problem for given data g in lp for p in a neighborhood of 2 also the oblique derivative problem for the system is studied furthermore some regularity results for the dirichlet problem are obtained

on the tangent space to the bmo teichmuller space abstract in a previous paper 31 we established the complex analytic manifold theory of the bmo teichmuller space in this paper we identify the function space which is the tangent space to the bmo teichmuller space

effect of distributive mass of spring on power flow in engineering test abstract mass of spring is always neglected in theoretical and simulative analysis while it may be a significance in practical engineering this paper is concerned with the distributive mass of a steel spring which is used as an isolator to simulate isolation performance of a water pipe in a heating system theoretical derivation of distributive mass effect of steel spring on vibration is presented and multiple eigenfrequencies are obtained which manifest that distributive mass results in extra modes and complex impedance properties furthermore numerical simulation visually shows several anti resonances of the steel spring corresponding to impedance and power flow curves when anti resonances emerge the spring collects large energy which may cause damage and unexpected consequences in practical engineering and needs to be avoided finally experimental tests are conducted and results show consistency with that of the simulation of the spring with distributive mass

a note on the bmo teichmuller space abstract astala zinsmeister 2 introduced a new topology on the set of all strongly quasisymmetric homeomorphisms of the unit circle denoted by sqs s 1 by means of bmo norm under this new topology we prove that sqs s 1 is a partial topological group and the characteristic topological subgroup of sqs s 1 consists of strongly symmetric homeomorphisms

polynomial growth estimates for multilinear singular integral operators on demontre un theoreme pour des mesures de carleson et on l applique a l operateur de kato en dimension 1 on demontre un critere de limitation general on donne une application aux commutateurs de coolderon on etudie les d commutateurs

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

divergence groups have the bowen property we show that every deformation of a divergence type fuchsian group has a limit set which is either a circle or has dimension strictly larger than 1 this is known to be false for all convergence type groups and hence solves bowen s problem in the general case the proof uses a theorem of dennis sullivan s about convex hulls in hyperbolic 3 space and we give a new simpler proof of this result as well

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

universal teichmuller space and bmo abstract we first give some new characterizations on bmoa teichmuller space and various characterizations on vmoa teichmuller space as well in particular we prove that a quasisymmetric conformal welding h corresponds to an asymptotically smooth curve in the sense of pommerenke 1978 32 precisely when h is absolutely continuous with log h vmo we then show that these bmo teichmuller spaces have natural complex structures

motif trie an efficient text index for pattern discovery with don t cares abstract we introduce the motif trie data structure which has applications in pattern matching and discovery in genomic analysis plagiarism detection data mining intrusion detection spam fighting and time series analysis to name a few here the extraction of recurring patterns in sequential and textual data is one of the main computational bottlenecks for this we address the problem of extracting maximal patterns with at most k don t care symbols and at least q occurrences according to a maximality notion we define we apply the motif trie to this problem also showing how to build it efficiently as a result we give the first algorithm that attains a stronger notion of output sensitivity where the cost for an input sequence of n symbols is proportional to the actual number of occurrences of each pattern which is at most n much smaller in practice this avoids the best known cost of o n c per pattern for constant c 1 which is otherwise impractical for massive sequences with large n

flexural intensity measurement on finite plates using modal spectrum ideal filtering abstract flexural intensities on various plate like structures with arbitrary boundary conditions are calculated using measured and fem yielded mobility in doing so a two dimensional spatial fourier transform has been implemented along with a refined k spectral filtering concept intensity is decomposed into individual contributions from bending moments twisting moments and shear forces the source and energy sink localization and energy flow have been analyzed through these contributions the effect of reflections from the plate edges and that of the uncorrelated noise on the intensity are discussed it is shown that the width of the k filters may have a non negligible influence on the shape of the intensity field damping in the structure can efficiently control the edge reflections and therefore help to localize the energy sources and sinks a link has been found at certain excitation conditions between the radiated acoustic intensity and the active flexural intensity it is also observed that the classical method of studying the vibration transmission using vibration amplitude measurements does not reflect the transmitted vibration energy but rather provides information on non propagating reactive energy the fem study further explains some of the experimental observations and suggests the possibility of applying intensity to complex analytical models

bmo teichmuller spaces revisited abstract in 6 the equivalence among three definitions of bmo teichmuller spaces associated with a fuchsian group was proven using the douady earle extension operator in this paper we show that these equivalences are actually biholomorphisms in 6 it was further shown that the douady earle extension operator is continuous at the origin we improve this result by showing g teaux differentiability at this point

weil petersson teichmuller space ii smoothness of flow curves of h32 vector fields abstract given a continuous vector field t of sobolev class h 3 2 on the unit circle s 1 the flow maps g t of the differential equation d d t t 0 are known to be quasisymmetric homeomorphisms very recently gay balmaz ratiu 15 conjectured that the flow curve g t is in the weil petersson class wp s 1 and is continuously differentiable with respect to the hilbert manifold structure of wp s 1 introduced by takhtajan teo 40 the first assertion had already been demonstrated in our previous paper 36 in this sequel to 36 we will continue to deal with the weil petersson class wp s 1 and completely solve this conjecture in the affirmative

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

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

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

necessary and sufficient conditions for absolute continuity of elliptic harmonic measure our purpose in this paper is to give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding poisson kernel for the dirichlet problem exist this condition on the coefficients is global continuity together with the additional property that the modulus of continuity along some nontangential direction at each boundary point be bounded uniformly in these points and directions by a function 7 t satisfying the dini type condition

global wellposedness of the 3 d full water wave problem we consider the problem of global in time existence and uniqueness of solutions of the 3 d infinite depth full water wave problem in the setting that the interface tends to the horizontal plane the velocity and acceleration on the interface tend to zero at spatial infinity we show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders for any initial interface that is sufficiently small in its steepness and velocity we show that there exists a unique smooth solution of the full water wave problem for all time and the solution decays at the rate 1 t

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

almost global wellposedness of the 2 d full water wave problem we consider the problem of global in time existence and uniqueness of solutions of the 2 d infinite depth full water wave equation it is known that this equation has a solution for a time period 0 t e for initial data of the form e where t depends only on in this paper we show that for such data there exists a unique solution for a time period 0 e t e this is achieved by better understandings of the nature of the nonlinearity of the full water wave equation

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

well posedness of the water waves equations 1 1 presentation of the problem the water waves problem for an ideal liquid consists of describing the motion of the free surface and the evolution of the velocity field of a layer of perfect incompressible irrotational fluid under the influence of gravity in this paper we restrict our attention to the case when the surface is a graph parameterized by a function x where t denotes the time variable and x xi xd rd the horizontal spatial variables the method developed here works equally well for any integer d 1 but the only physically relevant cases are of course d 1 and d 2 the layer of fluid is also delimited from below by a not necessarily flat bottom parameterized by a time independent function b x we denote by q t the fluid domain at time t the incompressibility of the fluids is expressed by 1 1 div v 0 in qu t 0

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 transport equation in the scaling invariant besov or essen janson peng xiao space abstract this paper addresses a well posedness of the weak solution to the transport equation describing how a scalar quantity is transported in a space with an initial data in the scaling invariant besov or essen janson peng xiao space via the boundedness of the left and right compositions acting on each space

well posedness in sobolev spaces of the full water wave problem in 3 d we consider the motion of the interface separating an inviscid incompressible irrotational fluid from a region of zero density in three dimensional space we assume that the fluid region is below the vacuum the fluid is under the influence of gravity and the surface tension is zero assume that the density of mass of the fluid is one the gravitational field is 0 0 1 the free interface is t at time t 0 and the fluid occupies the region t the motion of the fluid is described by vt v v 0 0 1 p on t t 0 euler s equation 1 1 div v 0 on t t 0 incompressible 1 2 curl v 0 on t t 0 irrotational 1 3 where v v1 v2 v3 is the fluid velocity p is the fluid pressure since we neglect the surface tension the pressure is zero on the interface so on the interface p 0 on t 1 4 1 v is tangent to the free surface t t 1 5 we want to find solutions of system 1 1 1 5 taking prescribed initial data such that for every fixed t 0 t approaches the xy plane at infinity and v x y z t 0 vt x y z t 0 as x y z since the fluid is assumed irrotational incompressible we can reduce the study of the entire motion to the motion of the free surface the above model is a 3 d water wave model it is generally known that when surface tension is neglected the motion of the interface between an inviscid fluid and vacuum under the influence of gravity can be subject to taylor instability 8 22 in a previous work 24 we studied the 2 dimensional water wave model we showed that for a 2 d water wave the sign condition relating to taylor instability always holds for nonself intersecting interface that is the motion of the interface is not subject to taylor instability we showed further that the 2 d full nonlinear water wave problem is uniquely solvable in sobolev spaces locally in time for any initially nonself intersecting interface earlier works on the well posedness in sobolev spaces of the 2 d water wave problem include nalimov 18 yosihara 25 and walter craig 6 where the main results concern the well posedness of the

a justification of the modulation approximation to the 3d full water wave problem we consider modulational solutions to the 3d inviscid incompressible irrotational infinite depth water wave problem neglecting surface tension for such solutions it is well known that one formally expects the modulation to be a profile traveling at group velocity and governed by a 2d hyperbolic cubic nonlinear schrodinger equation in this paper we justify this fact by providing rigorous error estimates in sobolev spaces we reproduce the multiscale calculation to derive an approximate wave packet like solution to the evolution equations with mild quadratic nonlinearities constructed by sijue wu then we use the energy method along with the method of normal forms to provide suitable a priori bounds on the difference between the true and approximate solutions

a criterion for the boundedness of singular integrals on hypersurfaces on donne des conditions geometriques sur une hypersurface de r n pour que certaines integrales singulieres sur cette hypersurface definissent des operateurs bornes sur l 2

boundary layer methods for lipschitz domains in riemannian manifolds abstract we extend to the variable coefficient case boundary layer techniques that have been successful in the treatment of the laplace equation and certain other constant coefficient elliptic partial differential equations on lipschitz domains in euclidean space we treat the laplace operator on lipschitz domains in a manifold with c 1 metric tensor and study the dirichlet neumann and oblique derivative boundary problems

quasiconformal mappings and ahlfors david curves we show that if p is a quasiconformal mapping of the plane whose dilatation satisfies a certain quadratic carleson measure condition relative to an ahlfors david curve f then p is differentiable almost everywhere on f and log ip l e bmo when f is chord arc we show that its image is a bishopjones curve if the carleson norm is small then we show that p is absolutely continuous on f the image of f is an ahlfors david curve and p ea where a e bmo with a small norm

on the waterbag continuum the aim of this paper is to study the existence of a classical solution for the waterbag model with a continuum of waterbags which can been viewed as an infinite dimensional system of first order conservation laws the waterbag model which constitutes a special class of exact weak solution of the vlasov equation is well known in plasma physics and its applications in gyrokinetic theory and laser plasma interaction are very promising the proof of the existence of a continuum of regular waterbags relies on a generalized definition of hyperbolicity for an integrodifferential hyperbolic system of equations some results in singular integral operators theory and harmonic analysis riemann hilbert boundary value problems and energy estimates