commutators and related operators on harmonic bergman space of rn 1 abstract we study commutators and related operators on harmonic bergman space the l 2 r n 1 closure of the null space of laplacian by decomposing l 2 r n 1 into the sum of null spaces of powers of laplacian and using the theory of paracommutators studied in jp we characterize harmonic symbols for which the associated commutators are bounded or compact operators associated to the div curl theorem in clms in the theory of compensated compactness are also characterized

adaptive grid generation from harmonic maps on reimannian manifolds abstract in this paper we describe a new method for generation of solution adaptive grids based on harmonic maps on riemannian manifolds the reliability of the method is assured by an existence and uniqueness theorem for one to one maps between multidimensional multiconnected domains we formulate an adaptive riemannian metric consistent with this theorem several examples demonstrating application of the developed procedure are provided

a characterization of bloch space and besov space on the unit disk of the complex plane a characterization for the membership of bloch space and analytic besov space is expressed extending known results

norm estimates for operators from hp to lq abstract we give upper and lower estimates of the norm of a bounded linear operator from the hardy space h p to l q in terms of the norm of the rows and the columns of its associated matrix in certain vector valued sequence spaces

on the membership of hankel operators in a class of lorentz ideals abstract recall that the lorentz ideal c p is the collection of operators a satisfying the condition a p j 1 j p 1 p s j a consider hankel operators h f h 2 s l 2 s d h 2 s where h 2 s is the hardy space on the unit sphere s in c n in this paper we characterize the membership h f c p 2 n p

the bergman space the bloch space and commutators of multiplication operators soit d le disque unite ouvert dans le plan complexe c soit h d l ensemble des fonctions analytiques bornees sur d on caracterise les fonctions feh d telles que t f t f tft f est un operateur compact ou t f est l operateur multiplication t f l a 2 l a 2 defini par t f g fg

on the variational approximation of combined second and fourth order geometric evolution equations we present a variational formulation of combined motion by minus the laplacian of curvature and mean curvature flow as well as related flows the proposed scheme covers both the closed curve case and the case of curves that are connected via triple or quadruple junction points or intersect the external boundary on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches the presented scheme has very good properties with respect to the equidistribution of mesh points and if applicable area conservation

a boundedness criterion for singular integral operators of convolution type on the fock space abstract we show that for an entire function belonging to the fock space f 2 c n on the complex euclidean space c n the integral operator s f z c n f w e z w z w d w z c n is bounded on f 2 c n if and only if there exists a function m l r n such that z r n m x e 2 x i 2 z 2 d x z c n here d w n e w 2 d w is the gaussian measure on c n with this characterization we are able to obtain some fundamental results of the operator s including the normality the c algebraic properties the spectrum and its compactness moreover we obtain the reducing subspaces of s in particular in the case n 1 we give a complete solution to an open problem proposed by k zhu for the fock space f 2 c on the complex plane c zhu 2015 30

on the numerical solution of one dimensional pdes using adaptive methods based on equidistribution numerical experiments are described that illustrate some important features of the performance of moving mesh methods for solving one dimensional partial differential equations pdes the particular method considered here is an adaptive finite difference method based on the equidistribution of a monitor function and it is one of the moving mesh methods proposed by w huang y ren and r d russell 1994 siam j numer anal 31 709 we show how the accuracy of the computations is strongly dependent on the choice of monitor function and we present a monitor function that yields an optimal rate of convergence motivated by efficiency considerations for problems in two or more space dimensions we demonstrate a robust and efficient algorithm in which the mesh equations are uncoupled from the physical pde the accuracy and efficiency of the various formulations of the algorithm are considered and a novel automatic time step control mechanism is integrated into the scheme

mobius invariant hilbert spaces of holomorphic functions in the unit ball of ⁿ we prove that there exists a unique hilbert space of holomorphic functions in the open unit ball of c n whose semi inner product is invariant under mobius transformations

manifold evolution with tangential redistribution of points in this paper we propose several techniques for tangential redistribution of points on evolving surfaces this is an important issue in numerical approximation of any lagrangian evolution model since the quality of the mesh has a significant impact on the result of the computation we explain the volume oriented and length oriented tangential redistribution methods in a general setting of an m dimensional manifold evolving in an n dimensional manifold then we apply the proposed techniques to several manifold evolution problems we explain the numerical approximation of the models and present experiments illustrating the performance of our redistribution techniques

operators on weighted bergman spaces 0 p leq 1 and applications we describe the boundedness of a linear operator from bp f d c analytic d 1 z 1 z f z da z 1 p for 0 p 1 under some conditions on the weight function into a general banach space x by means of the growth conditions at the boundary of certain fractional derivatives of a single x valued analytic function this in particular allows us to characterize the dual of bp for 0 p 1 and to give a formulation of generalized carleson measures in terms of the inclusion b1 l d we then apply the result to the study of multipliers hankel operators and composition operators acting on bp spaces 1991 math subject class primary 47b38 47b35 secondary 42a45

a higher order scheme for a tangentially stabilized plane curve shortening flow with a driving force we introduce a new higher order scheme for computing a tangentially stabilized curve shortening flow with a driving force represented by an intrinsic partial differential equation for an evolving curve position vector our new scheme is a combination of the explicit forward euler and the fully implicit backward euler schemes at any discrete time step the solution is found efficiently using a few semi implicit iterations basic properties of the new scheme are proved in the paper and its precision is tested by comparing the results with known analytical solutions for any choice of the time step the new higher order scheme gives exact radius of evolving uniformly discretized circles in case of flow by curvature and in case of rotation by a constant tangential velocity such properties do not hold for other schemes solving flow by mean curvature like the classical explicit semi implicit or fully implicit schemes in general the scheme is second order accurate which is shown by comparing a numerically evolving encompassed area with known analytical expression the behavior of the scheme is discussed on representative examples and its advantages with respect to the balance between cpu time and precision are shown

characterizations of certain classes of hankel operators on the bergman spaces of the unit disk let f be an integrable function on the unit disk the hankel operator hf is densely defined on the bergman space ap by hfg fg p fg where g is a bounded analytic function and p is the bergman projection orthogonal projection from l2 to a2 extended to l1 via its integral formula in this paper the functions f for which hf extends to a bounded operator from ap to lp are characterized 1 p also characterized are the functions f for which hf extends to a compact or schatten class operator on a2 the proofs can be extended to handle any smoothly bounded domain in c in place of the unit disk

moving mesh methods based on moving mesh partial differential equations several versions of a moving mesh method are developed based on a mesh spatial smoothing technique and on the moving mesh pdes derived in a previous paper these versions are quite simple and easy to program they are applied to three bench mark one dimensional problems which show different solution behaviour the numerical results clearly demonstrate that the present methods are capable of accurately tracking rapid spatial and temporal transitions

gleason parts and cop let h denote the banach algebra of bounded analytic functions on the open unit disc d and let m h denote the maximal ideal space of h one of the results in this paper shows that if two gleason parts in m h have distinct closures then there exists an h function which is identically zero on one part and nonzero on the other from this one obtains a corona theorem for certain subalgebras of h let cop denote the algebra of bounded analytic functions that are in the little bloch space it is shown here that there exists a cop function h and an inner function i such that i divides h in h1 but the result is not in cop

comments on a derivation and application of the maximum entropy production principle we show that 1 an error invalidates the derivation dewar 2005 j phys a math gen 38 l371 of the maximum entropy production maxep principle for systems far from equilibrium for which the constitutive relations are nonlinear and 2 the claim dewar 2003 j phys a math gen 36 631 that the phenomenon of self organized criticality is a consequence of maxep for slowly driven systems is unjustified

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

duality for logarithmic interpolation spaces when 0 q 1 and applications abstract we work with spaces a 0 a 1 q a which are logarithmic perturbations of the real interpolation spaces we determine the dual of a 0 a 1 q a when 0 q 1 as we show if 0 or 1 then the dual space depends on the relationship between q and a furthermore we apply the abstract results to compute the dual space of besov spaces of logarithmic smoothness and the dual space of spaces of compact operators in a hilbert space which are close to the macaev ideals

information theory explanation of the fluctuation theorem maximum entropy production and self organized criticality in non equilibrium stationary states jaynes information theory formalism of statistical mechanics is applied to the stationary states of open non equilibrium systems first it is shown that the probability distribution p of the underlying microscopic phase space trajectories over a time interval of length satisfies p exp 2kb where is the time averaged rate of entropy production of three consequences of this result are then derived 1 the fluctuation theorem which describes the exponentially declining probability of deviations from the second law of thermodynamics as 2 the selection principle of maximum entropy production for non equilibrium stationary states empirical support for which has been found in studies of phenomena as diverse as the earth s climate and crystal growth morphology and 3 the emergence of self organized criticality for flux driven systems in the slowly driven limit the explanation of these results on general information theoretic grounds underlines their relevance to a broad class of stationary non equilibrium systems in turn the accumulating empirical evidence for these results lends support to jaynes formalism as a common predictive framework for equilibrium and non equilibrium statistical mechanics

on the extreme of internal entropy production using the one dimensional diffusion equation the extrema of internal entropy production are investigated it is shown that the internal entropy production is essentially a convex function with only a minimum in euler variation with respect to temperature regardless of if the system is open or closed the maximum internal entropy production can only occur in variation with respect to a physical coefficient it is found that either a maximum or a minimum internal entropy production can occur with variation with respect to a diffusivity coefficient the maximum tends to occur for the closed boundary condition while the minimum tends to occur for the open boundary condition for a non steady state the study indicates that the extreme results shown in the steady state are not guaranteed to occur under the non steady condition the work highlights that the physics behind determining extrema of internal entropy production is still not fully understood

hankel operators and toeplitz operators on the bergman space abstract we consider in this paper the question of when the semi commutator t fg t f t g on the bergman space with bounded harmonic symbols is compact several conditions equivalent to compactness of t fg t f t g are given as a consequence we prove a conjecture of axler that for bounded analytic functions f and g on the unit disk t fg t g t f is compact iff either f or g is constant on each gleason part p m except d

hankel operators and the stieltjes moment problem let s be a non vanishing stieltjes moment sequence and let be a representing measure of it we denote by n the image measure in cn of n under the map t t where n is the rotation invariant probability measure on the unit sphere we show that the closure of holomorphic polynomials in l2 n is a reproducing kernel hilbert space of analytic functions and describe various spectral properties of the corresponding hankel operators with anti holomorphic symbols in particular if n 1 we prove that there are nontrivial hilbert schmidt hankel operators with anti holomorphic symbols if and only if s is exponentially bounded in this case the space of symbols of such operators is shown to be the classical dirichlet space we mention that the classical weighted bergman spaces the hardy space and fock type spaces fall in this setting

practical aspects of formulation and solution of moving mesh partial differential equations moving mesh partial differential equations mmpdes are used in the mmpde moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems how mmpdes are formulated and solved is crucial to the efficiency and robustness of the method in this paper several practical aspects of formulating and solving mmpdes are studied they include spatial balance scaling invariance effective control of mesh concentration bounds on time steps multiple sub steps and two level mesh movement numerical results are also given c 2001 academic press

numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh a finite difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two dimensional poisson equation s 0 where is a function of or its derivatives sis a function of position and or its normal derivative is specified on the boundary the finite difference equations are solved by successive overrelaxation the triangle mesh which is constructed numerically by solving laplace s equation is easily adapted to nonrectangular boundaries and interfaces examples of numerical results are given for the magnetostatic problem with iron and other possible applications are mentioned

hankel operators on the bergman space of bounded symmetric domains let q be a bounded symmetric domain in cin with normalized volume measure dv let p be the orthogonal projection from l 2 q d v onto the bergman space la q of holomorphic functions in l 2 q d v let a p be the orthogonal projection from l 2 q dv onto the closed subspace of antiholomorphic functions in l 2 2 d v the little hankel operator hf with symbol f is the operator from l2 q into l2 q d v defined by hfg p fg we characterize the boundedness compactness and membership in the schatten classes of the hankel operators hf in terms of a certain integral transform of the symbol f these characterizations are further studied in the special cases of the open unit ball and the poly disc in cn

schatten class membership of hankel operators on the unit sphere abstract let h 2 s be the hardy space on the unit sphere s in c n n 2 consider the hankel operator h f 1 p m f h 2 s where the symbol function f is allowed to be arbitrary in l 2 s d we show that for p 2 n h f is in the schatten class c p if and only if f p f belongs to the besov space b p to be more precise the if part of this statement is easy the main result of the paper is the only if part we also show that the membership h f c 2 n implies f p f 0 i e h f 0

modeling cell movement and chemotaxis using pseudopod based feedback a computational framework is presented for the simulation of eukaryotic cell migration and chemotaxis an empirical pattern formation model based on a system of nonlinear reaction diffusion equations is approximated on an evolving cell boundary using an arbitrary lagrangian eulerian surface finite element method ale sfem the solution state is used to drive a mechanical model of the protrusive and retractive forces exerted on the cell boundary movement of the cell is achieved using a level set method results are presented for cell migration with and without chemotaxis the simulated behavior is compared with experimental results of migrating dictyostelium discoideum cells

a hybrid numerical method for interfacial fluid flow with soluble surfactant we address a significant difficulty in the numerical computation of fluid interfaces with soluble surfactant that occurs in the physically representative limit of large bulk peclet number pe at the high values of pe in typical fluid surfactant systems there is a transition layer near the interface in which the surfactant concentration varies rapidly and large gradients at the interface must be resolved accurately to evaluate the exchange of surfactant between the interface and bulk flow we use the slenderness of the layer to develop a fast and accurate hybrid numerical method that incorporates a separate singular perturbation analysis of the dynamics in the transition layer into a full numerical solution of the interfacial free boundary problem the accuracy and efficiency of the method is assessed by comparison with a more traditional numerical approach that uses finite differences on a curvilinear coordinate system exterior to the bubble without the separate transition layer reduction the traditional method implemented here features a novel fast calculation of fluid velocity off the interface

function theory on cartan domains and the berezin toeplitz symbol calculus cn with dv z normalized lebesgue measure on 9 we let l l2 q dv be the usual space of lebesgue square integrable complex valued functions on 9 by h2 h2 q dv we denote the bergman subspace of l2 consisting of holomorphic functions the orthogonal projection operator from l2 onto h2 is denoted by p forf in l q the space of essentially bounded measurable functions on 9 we will consider the multiplication operator

moving mesh strategy based on a gradient flow equation for two dimensional problems in this paper we introduce a moving mesh method for solving pdes in two dimensions it can be viewed as a higher dimensional generalization of the moving mesh pde mmpde strategy developed in our previous work for one dimensional problems w huang y ren and r d russell siam j numer anal 31 1994 pp 709 730 the mmpde is derived from a gradient flow equation which arises using a mesh adaptation functional in turn motivated from the theory of harmonic maps geometrical interpretations are given for the gradient equation and functional and basic properties of this mmpde are discussed numerical examples are presented where the method is used both for mesh generation and for solving time dependent pdes the results demonstrate the potential of the mesh movement strategy to concentrate the mesh points so as to adapt to special problem features and to also preserve a suitable level of mesh orthogonality

bergman commutators and norm ideals let p be the orthogonal projection from l2 b dv onto the bergman space la2 b dv of the unit ball in cn in this paper we characterize the membership of commutators of the form mf p in the norm ideal c where the symmetric gauge function is allowed to be arbitrary

a new characterization of dirichlet type spaces on the unit ball of cn abstract in this paper a bmo type characterization of dirichlet type spaces d p on the unit ball of cn is given

generalizations of the forelli rudin estimates we give elementary proofs of the forelli rudin estimates and generalizations of these estimates as an application we obtain lp boundedness results for classes of integral operators that include bergman projections and hankel operators

diffusion on a curved surface coupled to diffusion in the volume an algorithm is presented for solving a diffusion equation on a curved surface coupled to diffusion in the volume a problem often arising in cell biology it applies to pixilated surfaces obtained from experimental images and performs at low computational cost in the method the laplace beltrami operator is approximated locally by the laplacian on the tangential plane and then a finite volume discretization scheme based on a voronoi decomposition is applied convergence studies show that mass conservation built in the discretization scheme and cancellation of sampling error ensure convergence of the solution in space with an order between 1 and 2 the method is applied to a cell biological problem where a signaling molecule g protein rac cycles between the cytoplasm and cell membrane thus coupling its diffusion in the membrane to that in the cell interior simulations on realistic cell geometry are performed to validate and determine the accuracy of a recently proposed simplified quantitative analysis of fluorescence loss in photobleaching the method is implemented within the virtual cell computational framework freely accessible at www vcell org

a computational method for the coupled solution of reaction diffusion equations on evolving domains and manifolds in this paper we devise a moving mesh finite element method for the approximate solution of coupled bulk surface reaction diffusion equations on an evolving two dimensional domain fundamental to the success of the method is the robust generation of bulk and surface meshes for this purpose we use a novel moving mesh partial differential equation mmpde approach the developed method is applied to model problems with known analytical solutions these experiments indicate second order spatial and temporal accuracy coupled bulk surface problems occur frequently in many areas in particular in the modelling of eukaryotic cell migration and chemotaxis we apply the method to a model of the two way interaction of a migrating cell in a chemotactic field where the bulk region corresponds to the extracellular region and the surface to the cell membrane

reproducing kernel functions and asymptotic expansions on jordan kepler manifolds abstract we study the complex geometry of generalized kepler manifolds defined in jordan theoretic terms introduce hilbert spaces of holomorphic functions defined by radial measures and find the complete asymptotic expansion of the corresponding reproducing kernels for kahler potentials both in the flat and bounded setting

the moving boundary node method a level set based finite volume algorithm with applications to cell motility eukaryotic cell crawling is a highly complex biophysical and biochemical process where deformation and motion of a cell are driven by internal biochemical regulation of a poroelastic cytoskeleton one challenge to built quantitative models that describe crawling cells is solving the reaction diffusion advection dynamics for the biochemical and cytoskeletal components of the cell inside its moving and deforming geometry here we develop an algorithm that uses the level set method to move the cell boundary and uses information stored in the distance map to construct a finite volume representation of the cell our method preserves cartesian connectivity of nodes in the finite volume representation while resolving the distorted cell geometry derivatives approximated using a taylor series expansion at finite volume interfaces lead to second order accuracy even on highly distorted quadrilateral elements a modified laplacian based interpolation scheme is developed that conserves mass while interpolating values onto nodes that join the cell interior as the boundary moves an implicit time stepping algorithm is used to maintain stability we use the algorithm to simulate two simple models for cellular crawling the first model uses depolymerization of the cytoskeleton to drive cell motility and suggests that the shape of a steady crawling cell is strongly dependent on the adhesion between the cell and the substrate in the second model we use a model for chemical signalling during chemotaxis to determine the shape of a crawling cell in a constant gradient and to show cellular response upon gradient reversal

continuity and schatten von neumann p class membership of hankel operators with anti holomorphic symbols on generalized fock spaces abstract in this paper we investigate hankel operators h f a m 2 a m 2 with anti holomorphic symbols f k 0 b k z k l 2 c z m where a m 2 are general fock spaces we will show that h f is not continuous if the corresponding symbol is not a polynomial f k 0 n b k z k for polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of n and m for monomials z k we will give a complete characterization of the schatten von neumann p class membership for p 0 namely in case 2 k m the hankel operators h z k are in the schatten von neumann p class iff p 2 m m 2 k and in case 2 k m they are not in the schatten von neumann p class

the dixmier trace of hankel operators on the bergman space abstract we give a formula for the dixmier trace of big hankel operators on the bergman space of the disk or of finitely connected domains for harmonic symbols we find the regularity required of the symbol for the formula to hold

paracommutators boundedness and schatten von neumann properties definition d une classe d operateurs denommes paracommutateurs operant sur les fonctions de l 2 r d par analogie avec la para multiplication de bony et les commutateurs des operateurs de calderon zygmund etablissement de la borne et des proprietes de schatten von neumann

a moving mesh finite element method for the two dimensional stefan problems an r adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of two dimensional heat conduction problems with a phase change the grid is obtained from a global mapping of the physical to the computational domain which is designed to cluster mesh points around the interface between the two phases of the material the enthalpy equation is discretised using a semiimplicit galerkin finite element method using linear basis functions the moving finite element method is applied to problems where the phase front is cusp shaped and where the interface changes topology

moving mesh partial differential equations mmpdes based on the equidistribution principle this paper considers several moving mesh partial differential equations that are related to the equidistribution principle several of these are new and some correspond to discrete moving mesh equations that have been used by others their stability is analyzed and it is seen that a key term for most of these moving mesh pdes is a source like term that measures the level of equidistribution it is shown that under weak assumptions mesh crossing cannot occur for most of them finally numerical experiments for these various moving mesh pdes are performed to study their relative properties

norm estimates for iterated commutators on the bergman spaces of the unit ball introduction we study the iterated commutators of the bergman projection and the multiplication by measurable functions called the symbols unlike the commutators the iterated commutators are no longer depending linearly on their symbols therefore most of the techniques used successfully in studying the first order commutators fail to work effectively for the nth order iterated commutators these operators are also very different from their analogs on l2 rm which has been studied by l peng t qian in pq using the s jason and j peeter s technique established in jp and r rochberg s semmes in rs where deeper tools of harmonic analysis in r are employed in this paper by using the bergman geometry properties of holomorphic functions and related analyses we characterize the conjugate holomorphic symbols for which the corresponding iterated commutators are bounded compact or in the schatten p class some lp estimates are also included in our discussion let 1m be the open unit ball of cm and dv z be the volume measure on blm

bounded symbols and reproducing kernel thesis for truncated toeplitz operators compressions of toeplitz operators to coinvariant subspaces of h2 are called truncated toeplitz operators we study two questions related to these operators the first raised by sarason is whether boundedness of the operator implies the existence of a bounded symbol the second is the reproducing kernel thesis we show that in general the answer to the first question is negative and we exhibit some classes of spaces for which the answers to both questions are positive

factorization of sturm liouville operators solvable potentials and underlying algebraic structure in this paper a general method of factorization of sturm liouville sl operators is provided a method to solve sl eigenvalue problems is presented new classes of exactly solvable potentials are obtained the supersymmetry and shape invariance approaches are generalized to the sl operators it is shown that the sl shape invariance potentials have an underlying algebraic structure this algebra is in general infinite dimensional the condition of finite algebra is obtained

maximum entropy production and the fluctuation theorem recently the author used an information theoretical formulation of non equilibrium statistical mechanics maxent to derive the fluctuation theorem ft concerning the probability of second law violating phase space paths a less rigorous argument leading to the variational principle of maximum entropy production mep was also given here a more rigorous and general mathematical derivation of mep from maxent is presented and the relationship between mep and the ft is thereby clarified specifically it is shown that the ft allows a general orthogonality property of maximum information entropy to be extended to entropy production itself from which mep then follows the new derivation highlights mep and the ft as generic properties of maxent probability distributions involving anti symmetric constraints independently of any physical interpretation physically mep applies to the entropy production of those macroscopic fluxes that are free to vary under the imposed constraints and corresponds to selection of the most probable macroscopic flux configuration in special cases maxent also leads to various upper bound transport principles the relationship between maxent and previous theories of irreversible processes due to onsager prigogine and ziegler is also clarified in the light of these results

bergman kernels tyz expansions and hankel operators on the kepler manifold for a class of o n 1 r invariant measures on the kepler manifold possessing finite moments of all orders we describe the reproducing kernels of the associated bergman spaces discuss the corresponding asymptotic expansions of tian yau zelditch and study the relevant hankel operators with conjugate holomorphic symbols related reproducing kernels on the minimal ball are also discussed finally we observe that the kepler manifold either does not admit balanced metrics or such metrics are not unique

bmo on strongly pseudoconvex domains hankel operators duality and overline partial estimates we study the condition that characterizes the symbols of bounded hankel operators on the bergman space of a strongly pseudoconvex domain and show that it is equivalent to bmo plus analytic here we mean the bergman metric bmo of berger coburn and zhu in the course of the proof we obtain new 0 estimates that may be of independent interest some applications include a decomposition of bmo similar to the classical li l and two characterizations of the dual of vmo which is also a predual of bmo in addition we obtain some partial results on the boundedness of hankel operators in l1 norm

characterizations for besov spaces and applications part i the main theorem of this paper gives a characterization for holomorphic besov space bp d over a large class of bounded domains d in cn which states that there is a bounded linear operator vd bp d lp d d so that pvd i on bp d where p is the bergman projection and d z k z z dv is the biholomorphic invariant measure with k z z being bergman kernel function for d moreover some application for characterizing schatter von neumann p class small hankel operation is given as a direct consequence of this theorem

simple computation of reaction diffusion processes on point clouds the study of reaction diffusion processes is much more complicated on general curved surfaces than on standard cartesian coordinate spaces here we show how to formulate and solve systems of reaction diffusion equations on surfaces in an extremely simple way using only the standard cartesian form of differential operators and a discrete unorganized point set to represent the surface our method decouples surface geometry from the underlying differential operators as a consequence it becomes possible to formulate and solve rather general reaction diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis to illustrate the generality of the method computations for surface diffusion pattern formation excitable media and bulk surface coupling are provided for a variety of complex point cloud surfaces

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

computational solution of two dimensional unsteady pdes using moving mesh methods numerical experiments are described which illustrate some important features of the performance of moving mesh methods for solving two dimensional partial differential equations pdes here we are concerned with algorithms based on moving mesh methods proposed by w huang and r d russell siam j sci comput 20 998 1999 we show that the accuracy of the computations is strongly influenced by the choice of monitor function and we present a monitor function which yields a higher rate of convergence than those that are commonly used in an earlier paper g beckett j a mackenzie a ramage and d m sloan j comput phys 167 372 2001 we demonstrated a robust and efficient algorithm for problems in one space dimension in which the mesh equation is decoupled from the physical pde and the time step is controlled automatically the present work extends this algorithm to deal with problems in two space dimensions

analytic besov spaces and hardy type inequalities in tube domains over symmetric cones we give various equivalent formulations to the partially open problem about l p boundedness of bergman projections in tubes over cones namely we show that such boundedness is equivalent to the duality identity between bergman spaces a p 0 a p and also to a hardy type inequality related to the wave operator we introduce analytic besov spaces in tubes over cones for which such hardy inequalities play an important role for p 2 we identify as a besov space the range of the bergman projection acting on l p and also the dual of a p 0 for the bloch space b 1 we give in addition new necessary conditions on the number of derivatives required in its deflnition

duality and hankel operators on the bergman spaces of bounded symmetric domains soit un domaine symetrique borne dans c n avec dv la mesure de volume normalisee l espace de bergman l a p est le sous espace clos de l p dv constitue des fonctions holomorphes on decrit le dual et le predual de l a 1 pour tous les domaines symetriques bornes

hankel operators induced by radial bekolle bonami weights on bergman spaces we study big hankel operators h f nu a p omega rightarrow l q nu generated by radial bekolle bonami weights nu when 1 p le q infty here the radial weight omega is assumed to satisfy a two sided doubling condition and a p omega denotes the corresponding weighted bergman space a characterization for simultaneous boundedness of h f nu and h overline f nu is provided in terms of a general weighted mean oscillation compared to the case of standard weights that was recently obtained by pau et al indiana univ math j 65 5 1639 1673 2016 the respective spaces depend on the weights omega and nu in an essentially stronger sense this makes our analysis deviate from the blueprint of this more classical setting as a consequence of our main result we also study the case of anti analytic symbols

a local inequality for hankel operators on the sphere and its application abstract let h 2 s be the hardy space on the unit sphere s in c n we establish a local inequality for hankel operators h f 1 p m f h 2 s as an application of this local inequality we characterize the membership of h f in the lorentz like ideal c p 2 n p