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．     

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.     

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     

Interpolation for martingale Hardy spaces over weighted measure spaces

Several interpolation theorems on martingale Hardy spaces over weighted measure spaces are given. Our proofs are based on the atomic decomposition of martingale Hardy spaces over weighted measure spaces. As applications of interpolation theorems, some inequalities of martingale transform operator are obtained.     

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.     

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.     

Bicomplex Weighted Hardy Spaces and Bicomplex <Emphasis Type="Italic">C</Emphasis>*-algebras

In this paper we study the bicomplex version of weighted Hardy spaces. Further, we describe reproducing kernels for the bicomplex weighted Hardy spaces. In particular, we generalize some results which holds for the classical weighted Hardy spaces. We also introduce the notion of bicomplex C*-algebra and discuss some of its properties.     

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.     

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.     

加权Herz型Hardy空间的分子刻画

首先定义了加权Herz型Hardy空间上的分子并证明了其分子刻画。作为应用,给出了强奇异积分算子T_b在加权Herz和Hardy空间上有界性的证明。     

From Nörlund matrices to Laplace representations

The existence of Laplace representations for functions in weighted Hardy spaces on the right half plane is established. The method uses an extension of an inequality involving Nörlund matrices and corresponding convolution operators on the line. Analogous inequalities are proved for power series representations of functions in weighted Hardy spaces on the disc.

     

On Hardy Inequality in Variable Lebesgue Spaces with Mixed Norm

In this paper a two-weight boundedness of multidimensional Hardy operator and its dual operator acting from one weighted variable Lebesgue spaces with mixed norm into other weighted variable Lebesgue spaces with mixed norm spaces is proved. In particular, a new type two-weight criterion for multidimensional Hardy operator is obtained.     

Hermitian Weighted Composition Operators and Bergman Extremal Functions

Weighted composition operators have been related to products of composition operators and their adjoints and to isometries of Hardy spaces. In this paper, Hermitian weighted composition operators on weighted Hardy spaces of the unit disk are studied. In particular, necessary conditions are provided for a weighted composition operator to be Hermitian on such spaces. On weighted Hardy spaces for which the kernel functions are ${(1 - \overline{w}z)^{-\kappa}}$ for κ ≥ 1, including the standard weight Bergman spaces, the Hermitian weighted composition operators are explicitly identified and their spectra and spectral decompositions are described. Some of these Hermitian operators are part of a family of closely related normal weighted composition operators. In addition, as a consequence of the properties of weighted composition operators, we compute the extremal functions for the subspaces associated with the usual atomic inner functions for these weighted Bergman spaces and we also get explicit formulas for the projections of the kernel functions on these subspaces.     

Characterizations of weighted Besov and Triebel-Lizorkin spaces via temperatures

Hardy-Littlewood type characterizations (via temperatures on a half-space) of weighted Besov and Triebel-Lizorkin spaces studied recently by the author are given. In the proof of the sufficient parts of the results, a “sub-mean-value property” of temperatures is used in an elegant way to get control of certain terms by the Hardy maximal function or its vector-valued version. As a byproduct of the results, another characterization of weighted Hardy spaces as well as characterizations of the Gauss-Weierstrass integrals on a strip domain of distributions in the above weighted spaces is obtained also.     

Hardy–Carleson Measures and Their Dual Poisson–Szegö Transforms

Recently Choe et al. have introduced the notion of dual Berezin transforms and used it to obtain new characterizations of the Carleson measures for the weighted Bergman spaces over the unit ball in C ⁿ . Continuing our investigation on the Hardy spaces, we obtain new characterizations of the Carleson measures for the Hardy spaces by means of the dual Poisson–Szegö transforms introduced by Koosis. Compared with the results for the weighted Bergman spaces, our results for the Hardy spaces not only show an similarity, but also reveal a new characterization.     

Weighted Hardy operators and commutators on Morrey spaces

The operator norms of weighted Hardy operators on Morrey spaces are worked out. The other purpose of this paper is to establish a sufficient and necessary condition on weight functions which ensures the boundedness of the commutators of weighted Hardy operators (with symbols in BMO(ℝ ⁿ )) on Morrey spaces.     

Weighted estimates for parametrized Littlewood-Paley operators

In this paper, we obtain some boundedness on the weighted Lebesgue spaces and the weighted Hardy spaces for the parametrized Littlewood-Paley operators with the kernel Ω satisfying the logarithmic type Lipschitz conditions.     

Corrections to the paper “The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces”

In this paper the author proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with variable exponent. As an application he proved the boundedness of certain sublinear operators on the weighted variable Lebesgue space. The proof of the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent does not contain any mistakes. But in the proof of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in my paper, which was published as R.A.Bandaliev, The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces, Czech. Math. J. 60 (2010), 327–337.     

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.     

Markov Chain Approximation of Pure Jump Processes

We prove the weighted endpoint estimates for some multilinear operators related to certain singular integral operators on some Hardy and Herz type Hardy spaces.