带振荡核奇异积分算子交换子在加权Morrey空间中的有界性质

本文研究Morrey空间中的交换子有界性的问题.利用John-Nirenberg不等式等工具建立带振荡核的奇异积分算子与BMO函数生成交换子在加权Morrey空间中的加权估计.     

Weighted Estimates of Variable Kernel Fractional Integral and Its Commutators on Vanishing Generalized Morrey Spaces with Variable Exponent

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent generalized weighted Morrey spaces and the variable exponent vanishing generalized weighted Morrey spaces. And the corresponding commutators generated by BMO function are also considered.     

NEW WEIGHTED MULTILINEAR OPERATORS AND COMMUTATORS OF HARDY-CESàRO TYPE

This paper deals with a general class of weighted multilinear Hardy-Cesaro operators that acts on the product of Lebesgue spaces and central Morrey spaces.Their sharp bounds are also obtained.In addition,we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro operators(with symbols in central BMO spaces) are bounded on the product of central Morrey spaces.These results extends known results on multilinear Hardy operators.     

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.     

振荡积分算子及其交换子在加权Morrey空间上的有界性质

振荡积分算子的有界性质是调和分析研究的中心内容之一. 本文得到了由Ricci 和Stein 定义的一类振荡积分算子在加权Morrey 空间中的强型、弱型估计. 在此基础上, 得到了该类振荡积分算子与BMO 函数生成的交换子的强型估计, 还建立了分数次振荡积分算子的对应结果.     

Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds,the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases,we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control,then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.     

Estimates for vector-valued commutators on weighted Morrey space and applications

In this paper, we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces. Applications to Calderón-Zygmund singular integral operators, oscillatory singular integral operators and parabolic difference equations are considered.     

Generalized Weighted Morrey Estimates for Marcinkiewicz Integrals with Rough Kernel Associated with Schrödinger Operator and Their Commutators

Let L =-?+V(x) be a Schr?dinger operator, where ? is the Laplacian on ■~n,while nonnegative potential V(x) belonging to the reverse H?lder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schr?dinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.     

Bounds of <Emphasis Type="Italic">p</Emphasis>-adic weighted Hardy-Cesàro operators and their commutators on <Emphasis Type="Italic">p</Emphasis>-adic weighted spaces of Morrey types

In this paper we aim to investigate the boundedness of the p-adic weighted Hardy-Cesàro operators and their commutators on weighted functional spaces of Morrey type. In each case, we obtain the corresponding operator norms.     

Norm Inequalities in Generalized Morrey Spaces

We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces.     

Variation Inequalities Related to Schr?dinger Operators on Morrey Spaces

The authors establish the boundedness of the variation operators associated with the heat semigroup, Riesz transforms and commutators generated by the Riesz transforms and BMO-type functions in the Schr?dinger setting on the Morrey spaces.     

Variation Inequalities Related to Schr\"odinger Operators on Morrey Spaces

The authors establish the boundedness of the variation operators associated with the heat semigroup, Riesz transforms and commutators generated by the Riesz transforms and BMO-type functions in the Schrödinger setting on the Morrey spaces.     

Weighted Estimates for Commutators of Strongly Singular Calderón–Zygmund Operators

In this paper,the authors establish the boundedness of commutators generated by strongly singular Calderón–Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces.Moreover,the corresponding results for commutators generated by strongly singular Calderón–Zygmund operators and weighted Lipschitz functions can also be obtained.     

单边奇异积分交换子的加权变差不等式

本文主要研究了单边Calder\''{o}n-Zygmund奇异积分交换子的加权变差不等式,即建立了单边Calder\''{o}n-Zygmund奇异积分与Lipschitz函数生成的交换子的加权变差不等式, 同时,利用权的外推法得到了该交换子在Triebel-Lizorkin空间上的加权变差不等式.     

广义Morrey空间上的奇异积分多线性交换子

本文得到了具有混合齐次变量核的奇异积分算子的多线性交换子在广义Morrey空间和加权 Lebesgue空间上的有界性．     

Weighted Estimates for Commutators of Hausdorff Operators on the Heisenberg Group

The aim of this paper is to give some sufficient conditions for the boundedness of commutators of Hausdorff operators with symbols in weighted central BMO type spaces on the Herz spaces, central Morrey spaces and Morrey-Herz spaces associated with both power weights and Muckenhoupt weights on the Heisenberg group.

     

单边Triebel-Lizorkin空间及其应用

引进了一类单边Tiebel-Lizorkin空间.在单边的意义下,利用权的外推法,得到了由CalderónZygmund奇异积分算子与Lipschjtz函数生成的交换子从加权Lebesgue空间到加权Triebel-Lizorkin 空间的有界性质.同时研究了单边分数次积分算子交换子的有关性质.     

Bounds of weighted multilinear Hardy-Cesàro operators in p-adic functional spaces

We introduce the p-adic weighted multilinear Hardy-Cesàro operator. We also obtain the necessary and sufficient conditions on weight functions to ensure the boundedness of that operator on the product of Lebesgue spaces, Morrey spaces, and central bounded mean oscillation spaces. In each case, we obtain the corresponding operator norms. We also characterize the good weights for the boundedness of the commutator of weighted multilinear Hardy-Cesàro operator on the product of central Morrey spaces with symbols in central bounded mean oscillation spaces.     

Bounds of weighted multilinear Hardy-Cesàro operators in <Emphasis Type="Italic">p</Emphasis>-adic functional spaces

We introduce the p-adic weighted multilinear Hardy-Cesàro operator. We also obtain the necessary and sufficient conditions on weight functions to ensure the boundedness of that operator on the product of Lebesgue spaces, Morrey spaces, and central bounded mean oscillation spaces. In each case, we obtain the corresponding operator norms. We also characterize the good weights for the boundedness of the commutator of weighted multilinear Hardy-Cesàro operator on the product of central Morrey spaces with symbols in central bounded mean oscillation spaces.     

Rough operators and commutators on homogeneous weighted Herz spaces

The authors establish the boundedness on homogeneous weighted Herz spaces for a large class of rough grals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.