Bilinear Operators on Herz-type Hardy Spaces on Locally Compact Vilenkin Groups

Let G be a locally compact Vilenkin group. In this paper the authors study the boundedness of bilinear operators B（f, g） given by finite sums of products of Calderdn-Zygmund operators in Herz space and Herz-type Hardy space on G. And an example, the boundedness from the products of Herz space to Herz-type Hardy space is given in the last section.     

RECURRENCE FOR WEIGHTED TRANSLATIONS ON GROUPS

Let G be a locally compact group, and let 1 ≤ p ∞. We characterize topologically multiply recurrent weighted translation operators on L~p(G) in terms of the Haar measure and the weight function. We also show that there do not exist any recurrent weighted translation operators on L~∞(G).     

COMMUTATORS OF GENERALIZED HARDY OPERATORS ON HOMOGENEOUS GROUPS

Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.     

BOUNDEDNESS OF FRACTIONAL INTEGRAL OPERATORS IN HERZ—TYPE SPACES ON LOCALLY COMPACT VILENKIN GROUPS

Let G be a locally compact Vilenkin group.In this paper we first establish the Hardy-Littlewood-Sobolev theorem on G.Then some boundedness theorems of fractional integral operators in Herz-type spaces on G are obtained.     

BOUNDEDNESS OF FRACTIONAL INTEGRAL OPERATORS IN HERZ-TYPE SPACES ON LOCALLY COMPACT VILENKIN GROUPS

Let G be a locally compact Vilenkin group. In this paper we first establish the Hardy-Littlewood-Sobolev theorem on G. Then some boundedness theorems of fractional integral operators in Herz-type spaces on G are obtained.     

Herz-type Hardy spaces on Vilenkin groups and their applications

Let 1＜q＜∞, 1-1/q≤α＜∞, 0＜p＜∞ and G be a locally compact Vilenkin group.The authors first introduce the general Herz-type Hardy spaces HKα,pq(G) and hKα,pq(G), then present the central atom or the central block and atom decompositions of these spaces. Using this characterization, they discuss some properties of these spaces and investigate the boundedness on the spaces HKα,pq(G) of the fractional integral operators and the boundedness on the spaces hKα,pq(G) of the pseudo-differential operators of order zero.     

Boundedness of fractional integral operators in Herz-type spaces on locally compact Vilenkin groups

Let G be a locally compact Vilenkin group. In this paper we first establish the Hardy-Littlewood-Sobolev theorem on G. Then some boundedness theorems of fractional integral operators in Herz-type spaceson G are obtained.     

λ-central BMO estimates for commutators of singular integral operators with rough kernels

The authors establish λ-central BMO estimates for commutators of singular integral operators with rough kernels on central Morrey spaces. Moreover, the boundedness of a class of multisublinear operators on the product of central Morrey spaces is discussed. As its special cases, the corresponding results of multilinear Calderon-Zygmund operators and multilinear fractional integral operators can be deduced, resDectivelv.     

Commutators of Calderón-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrödinger operators

Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.     

无限维测度空间上的微分演算(Ⅰ)

As a generalization of Guassian measures, CM-measures on R~∞ are presented here. We study the cores of Laplace-Beltrami operators with respeot to them and the commutative relations between differential operators on R~∞ and the symmetric diffusion semi-groups generated by the Lallace-Beltrami operators. Using these results, the Littlwood-Paley inequlities will be established in the following paper on more general measure spaces than Wiener space.     

齐次群上多线性奇异积分算子的有界性

Let G be a homogeneous group.In this paper,the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G.As its special case,the corresponding result of multilinear Calderón-Zygmund operators can be obtained.     

Decomposition of the Space of Regular Operators

Let E be a directed vector space with the Riesz decomposition property and F be a complete v?ctor lattice. It is proved that if G is a solid subspace of E then the subspace of all regular operators annihilating on G is a component in the space of all regular operators from E into F.¹²     

有界局部紧Vilenkin群上的广义Calderón-Zygmund算子(英文)

记Ｇ为一有界局部紧的Ｖｉｌｅｎｋｉｎ群．我们引进了Ｇ上的一类Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ型算子,并且证明了它们的加权ＬＰ（Ｇ）有界性．另外还给出了这些结果的一些应用．     

包含紧算子理想的Toeplitz算子代数的刻画

设G为一个torsion-free的离散群,（G,G＋）为一个拟序群,记T^G (G)为相应的Toeplitz算子代数,K(l^2(G 1)为l^2(G )上的紧算子全体,本文证明了K(l^2(G ))增包含于T^G (G)当且仅当下列两个条件时满足。（1）（G,G＋）为一个序群,（2）G中存在一个最小的正元。     

某些算子在局部紧的Vilenkin群上的Herz型Hardy空间

G表示局部紧的Vilenkin群， 在论文中作者将研究某些次线性算子和Calderón Zygmund算子在Herz型Hardy空间上的有界性.      

On the sharpness of non-optimal approximation for semigroup operators

The sharpness of the rate of approximation by certain operators to the identity is considered in the sense that there exist smooth elements such that a rate (given by a direct theorem) cannot be improved. The operators dealt with are semigroup operators, the Cesàro means of these, as well as the associated resolvent operators.Dedicated to Professor H. G. Tillmann on the occasion of his 60th birthday on Sept. 30, 1984, in friendship and admiration     

Some Remarks on Singular Integrals and Power Weights on Vilenkin Groups

Let G be a Vilenkin group and T a sublinear operator. The author investigates under what weak conditions on the size of T, the Lp(G)-boundedness of T implies its Lp|x|α (G)-boundedness. For those sublinear operators which map Lp(G) to Lq(G) with p < q the author also obtains some similar results.     

Best approximation by polynomial operators in banach spaces

The problem of approximation in the space of bounded linear operators ? (E;G) between normed spaces E and G by compact operators has been extensively studied in the last few years.

Recently Deutsch, Mach and Saatkamp ([2]) have considered the problem of approximating elements of ?(E;G) by the subset K _N(E;G) of operators whose range is at most N dimensional. We consider in this paper the problem of approximating operators (not necessarily linear) beteen normed spaces E and G by continuous homogeneous polynomials, and in particular by such polynomials which have finite-dimensional range.