Calderón – Zygmund Operators on Weighted Weak Hardy Spaces in Locally Compact Vilenkin Groups

Let G be a bounded locally compact Vilenkin group. We study the atomic decom‐position of weighted weak Hardy space. We also define several Calderón – Zygmund type operators and study their boundedness on, spaces like weighted Hardy spaces, weighted weak Hardy spaces and weighted weak Lebesgue spaces. Sharpness of some of our results is also discussed.     

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.     

Herz型空间中的Littlewood-Paley g函数

本文研究了包含 Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙ ｇ函数在内的一大类次线性算子从 Ｈｅｒｚ 空间到弱Ｈｅｒｚ空间ＷＫ中的有界 性;而当时,我们得到了ｇ函数从 Ｈｅｒｚ型 Ｈａｒｄｙ空间 ＨＫ（Ｒｎ）到 Ｈｅｒｚ空间或弱Ｈｅｒｚ空间ＷＫ（Ｒｎ）中的有界性．     

Weighted Composition Operators between Different Hardy Spaces

Let and be two analytic functions defined on such that. The operator given by is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continuity of weighted composition operators from a Hardy space H _p into another Hardy space H _q . We apply these results to study composition operators on Hardy spaces of a half-plane. Submitted: November 20, 2001.     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

A type theorem on the weighted Herz‐type Hardy spaces and applications

This paper gives a type theorem, which is a boundedness criterion for singular integral operators from the weighted Herz‐type Hardy spaces into the weighted local Herz‐type Hardy spaces. As applications, the corresponding mapping properties for the Cauchy integral and Calderón's commutators are obtained. In addition, a counter example is shown that neither is a Calderón–Zygmund singular integral operator bounded on the homogeneous local Herz‐type Hardy space, nor bounded on the classical local Hardy space.     

Boundedness of Sublinear Operators in Herz Spaces on Vilenkin Groups and its Application

The authors establish the boundedness of some sublinear operators in weighted Herz spaces on Vilenkin groups under certain weak local hypotheses on the size of these operators at the identity. This class of operators includes most of the important operators in harmonic analysis on Vilenkin groups. The main theorems are best possible under the conditions of the theorems. As applications, the authors establish the Littlewood-Paley function characterization of some Herz spaces and the relations between Herz spaces and Herz-type Hardy spaces.     

广义分数次积分算子在加权Herz型Hardy空间的有界性

利用加权Herz型Hardy空间的原子分解理论,讨论了广义分数次积分算子Tl从加权Lp空间到加权Lq空间,以及从加权Herz型Hardy空间到加权Herz空间的有界性问题.将已有的分数次积分算子的结论推广到广义分数次积分算子的情形.     

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.     

Weak type estimates for Calderón‐Zygmund operators on Herz spaces at critical indexes

We define weak Herz spaces (?ⁿ) which are the weak version of the ordinary Herz spaces (?ⁿ). We consider the boundedness of Calderón‐Zygmund operators from to at critical indexes α = ?n/q, n(1? 1/q) and q = 1. We also consider weighted estimates. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Singular integrals and commutators on homogeneous groups

Let G be a homogeneous group. In this paper, the authors establish several general theorems for the boundedness of sublinear operators and commutators generated by linear operators and BMO(G)functions on the weighted Lebesgue space on G. The conditions of these theorems are satisfied by many important operators in analysis and these operators satisfy only some weak conditions on the size of operators and are known to be bounded in the unweighted case. Some of these theorems are best possible even when G is the Euclidean space. The authors also give some applications of their theorems to the boundedness on weighted spaces of rough singular integrals, oscillatory integrals, parabolic singular integrals, their commutators and the maximal operators associated with them.     

Boundedness of generalized fractional integrals in weighted Herz-type spaces

In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights.     

带有加权Lipschitz函数的交换子的有界性

研究了由加权Lipschitz函数b和Calderón-Zygmund奇异积分算子T生成的交换子Tb在一些加权空间上的有界性,涉及到加权Hardy空间,加权Herz空间及和加权Herz型Hardy空间.同时也得到了其相应的端点估计.     

Calderón-Zygmund operaors on the Hardy spaces of weighted Herz type

Applying the decomposition theorems in [1] and [2], we obtain the boundedness theorem of Calderón-Zygmund operator of type δ on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear operators on the weighted Herz spaces. Supported by NSF of China and the Fund of Doctoral Program of N.E.C.     

Boundedness of generalized fractional integrals in weighted Herz-type spaces

In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights. This project was partially supported by the SEDF and the NNSF of China.     

Hausdorff Operators on Function Spaces

The authors mainly study the Hausdorff operators on Euclidean space Rn.They establish boundedness of the Hausdorff operators in various function spaces,such as Lebesgue spaces,Hardy spaces,local Hardy ...     

Calderón-Zygmund-Type Operators on Weighted Weak Hardy Spaces over ℝn

We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted Lebesgue spaces, weighted weak Lebesgue spaces, weighted Hardy spaces and weighted weak Hardy spaces. The sharpness of some results is also investigated. Received December 1, 1998, Revised May 2, 1999, Accepted May 19, 1999     

带有齐性核的分数次积分算子在Hardy型空间上的有界性

该文研究了带有齐性核的分数次积分算子T_(Ω,α)在一些Hardy空间上的映射性质,其中核Ω在球面S~(n-1)上满足一些L~S-Dini条件.作者将前人的一些结果改进到0αn情形,同时还得到了算子T_(Ω,α)在Herz型Hardy空间上的一个端点估计.     

R~n上加权弱Hardy空间中的Calderón-Zygmund型算子

作者引进了某些 Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ型算子,并且讨论了它们在加权 Ｌｅｂｅｓｇｕｅ空间、加权弱Ｌｅｂｅｓｇｕｅ空间、加权Ｈａｒｄｙ空间和加权弱Ｈａｒｄｙ空间上的有界性．作者也考察了一些结果的尖锐性．     

次线性算子在Herz型Hardy空间上的有界性

本文得到了一类次线性算子在Herz型Hardy空间上的有界性判定条件,该算子包括调和分析中许多重要的算子,同时还证明了Bochner-Riesz算子在Herz型Hardy空间上的有界性.