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

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

some new characterizations of dirichlet type spaces on the unit ball of cn abstract the dirichlet type spaces on the unit ball of c n are characterized by some oscillations in the bergman metric in this paper as an application of these new characterizations of dirichlet type spaces we prove that composition operators induced by biholomorphic maps are bounded on d p 1 p n

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

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

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

convergence of implicit finite difference methods applied to nonlinear mixed systems a new technique to prove convergence of finite difference methods applied to nonlinear pdes arising in computational fluid dynamics is presented the underlying systems may be hyperbolic parabolic or of mixed type like the navier stokes equations implicit finite difference methods are analyzed the essential idea leading to success is the introduction of a pilot function that is highly attractive to the numerical approximation and converges itself to the solution of the underlying system

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

unipotent hecke algebras of gln fq this paper describes a family of hecke algebras h endg indug where u is the subgroup of unipotent upper triangular matrices of g gln fq and is a linear character of u the main results combinatorially index a basis of h provide a large commutative subalgebra of h and after describing the combinatorics associated with the representation theory of h generalize the rsk correspondence that is typically found in the representation theory of the symmetric group

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

a theoretical framework for proving accuracy results for deferred corrections general techniques are described for proving accuracy results for deferred correction solutions to differential equations these techniques apply also to computational estimates of the local discretization error the proofs avoid the necessity of demonstrating the existence of asymptotic expansions of the global error in powers of some meshsize parameter

notes on the norm map between the hecke algebras of the gelfand graev representations of gl 2 q2 and u 2 q abstract let g be a connected reductive algebraic group defined over the field f q and let f and f be two frobenius maps such that f m f m for some integer m let g f g f and g f m g f m be the finite groups of fixed points in this article we consider the case where g gl 2 f q f is the usual frobenius map so that g f gl 2 q and f is the twisted frobenius map such that g f u n q in this case f 2 f 2 and g f 2 g f 2 gl 2 q 2 this article provides connections between the complex representation theory of these groups using the norm maps see c curtis t shoji a norm map for endomorphism algebras of gelfand graev representations in progr math vol 141 1997 pp 185 194 from the gelfand graev hecke algebra of gl 2 q 2 to the gelfand graev hecke algebras of both gl 2 q and u 2 q

the principle of the difference of difference quotients as a key to the self adaptive solution of nonlinear partial differential equations abstract a unified method for the numerical solution of nonlinear ordinary and partial differential equations elliptic and parabolic is developed the discretization error is estimated from the difference of difference quotients of a family of difference formulae the difference grid and the difference star of arbitrary order are self adapted and selected so that an optimum method results in which all error terms are well balanced to a prescribed relative tolerance

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

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

characterizations of q p spaces in the unit ball of c n abstract let b denote the unit ball of c n for 0 p the holomorphic function spaces q p and q p 0 on the unit ball of c n are defined as f q p sup a b b f z 2 g p z a d z and f q p 0 lim a 1 b f z 2 g p z a d z 0 in this paper we give some derivative free mixture and oscillation characterizations for q p and q p 0 spaces in the unit ball of c n

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

the generalized gelfand graev representations of u 3 q abstract there are three distinct generalized gelfand graev representations of the unitary group u 3 q one is the regular representation and one is the usual gelfand graev representation the third generalized gelfand graev representation is the one we examine in this paper

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

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

on the method of modified equations v asymptotic analysis of and direct correction and asymptotic successive correction techniques for the implicit midpoint method the equivalent second equivalent and simply modified equations for the implicit midpoint rule are shown to be asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step size as small parameter yields exactly the same results for linear problems with constant coefficients they are also equivalent to the original finite difference scheme straightforward regular multiple scales and summed up asymptotic techniques are used for the analysis of the implicit midpoint rule difference method and the accuracy of the resulting asymptotic expansion is assessed for several first order non linear autonomous ordinary differential equations it is shown that when the resulting asymptotic expansion is uniformly valid the asymptotic method yields very accurate results if the solution of the leading order equation is smooth and does not blow up the modified equation is also studied as a method for the development of new numerical schemes based on both direct correction and asymptotic successive correction techniques applied to the three kinds of modified equations the linear stability of these techniques is analyzed and their results are compared with those of runge kutta schemes for several autonomous and non autonomous first order ordinary differential equations

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

the gelfand graev representation of u 3 q abstract in this paper we explicitly calculate the irreducible representations of the endomorphism algebra of the gelfand graev representation of the unitary group u 3 q in addition we compute the structure constants of this endomorhphism algebra

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

on the numerical integration of nonlinear two point boundary value problems using iterated deferred corrections part 2 the development and analysis of highly stable deferred correction formulae iterated deferred correction methods have been very widely used for the numerical solution of general nonlinear two point boundary value problems in ordinary differential equations however there

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

on the method of modified equations vi asymptotic analysis of and asymptotic successive corrections techniques for two point boundary value problems in ode s the modified equation technique is extended to two point boundary value problems and a second order accurate implicit centered finite difference scheme for non homogeneous second order ordinary differential equations with linear boundary conditions is analyzed the first second and third modified equations or equivalent second equivalent and simply modified equations respectively for this scheme and its boundary conditions are presented it is shown that the three kinds of modified equations are asymptotically equivalent when the equivalent equation is used for the boundary conditions since an asymptotic analysis of these equations with the grid size as small parameter yields exactly the same results for a linear problem multiple scales and summed up asymptotic techniques are used and the resulting uniform asymptotic expansions are shown to be equivalent to the solution of the original finite difference scheme asymptotic successive corrections techniques are also applied to the three kinds of modified equations to obtain higher order schemes higher order boundary conditions are easily treated in the asymptotic successive corrections technique although these boundary conditions must be obtained by using the equivalent equation in order to obtain a correct estimate of the global error near the domain boundaries the methods introduced in this paper are applied to homogeneous and non homogeneous second order linear and non linear ordinary differential equations and yield very accurate results

on the method of modified equations i asymptotic analysis of the euler forward difference method the method of modified equations is studied as a technique for the analysis of finite difference equations the non uniqueness of the modified equation of a difference method is stressed and three kinds of modified equations are introduced the first modified or equivalent equation is the natural pseudo differential operator associated to the original numerical method linear and nonlinear combinations of the equivalent equation and their derivatives yield the second modified or second equivalent equation and the third modified or simply modified equation respectively for linear problems with constant coefficients the three kinds of modified equations are equivalent among them and to the original difference scheme for nonlinear problems the three kinds of modified equations are asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step as small parameter yields exactly the same results in this paper both regular and multiple scales asymptotic techniques are used for the analysis of the euler forward difference method and the resulting asymptotic expansions are verified for several nonlinear autonomous ordinary differential equations it is shown that when the resulting asymptotic expansion is uniformly valid the asymptotic method yields very accurate results if the solution of the leading order equation is smooth and does not blow up even for large step sizes

spaces m dp bnp and qp abstract in this paper the relations between d p and b n p m d p and b n p are discussed by means of high order radial derivative and random series the main results of this paper are 1 let i if 0 b n q d p ii if n p 2 q b n q and d p cannot included each other iii if q 3n p 2 then d p b n q 2 let 0 i if 0 b n q m d p ii if n p 2 q b n q and m d p cannot included each other iii if q 3n p 2 then m d p b n q 3 let n 1 n m d n 1 p q p

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

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

a skein like multiplication algorithm for unipotent hecke algebras let g be a finite group of lie type e g gl n fq and u a maximal unipotent subgroup of g if is a linear character of u then the unipotent hecke algebra is h end cg ind g u unipotent hecke algebras have a natural basis coming from double cosets of u in g this paper describes relations for reducing products of basis elements and gives a detailed description of the implications in the case g gl n f q

on the method of modified equations iii numerical techniques based on the second equivalent equation for the euler forward difference method new numerical successive correction techniques for ordinary differential equations based on the euler forward explicit method and the first modified or equivalent equation are presented these techniques are similar to iterative updating deferred methods and are based on the application of asymptotic methods to modified equations which do not require initial conditions for the high order derivatives in the truncation terms and which yield stable numerical methods it is shown that depending on the discretization of the high order derivatives in the high order correction equations different methods of as high order of consistency as required can be developed in this paper backward and centered formulas are used but the resulting numerical methods are not self starting it is shown that if the starting procedure is not adequate the numerical order of the method can be smaller than the theoretical one in order to avoid this loss of numerical order a method for consistently starting the asymptotic successive correction technique based on the use of fictitious times is presented and applied to autonomous and non autonomous ordinary differential equations and compared with the results of second and fourth order runge kutta methods it is shown that the fourth order runge kutta method is more accurate than the successive correction techniques for large time steps due to the higher order derivatives in the successive correction but for sufficiently small time steps these techniques have almost the same accuracy as the fourth order runge kutta method

asymptotic analysis of finite difference methods with this article we want to advocate the use of asymptotic methods for the analysis of finite difference schemes we present several examples to demonstrate the applicability of the approach advantages over the modified equation and truncation error analysis are pointed out