广义加权极大Morrey空间中次线性算子的有界性质

该文给出定义在R~n上的一类广义加权极大Morrey空间.证明一类次线性算子,包括分数次积分算子,在该类空间中的有界性质.同时还研究该类次线性算子的交换子在广义加权极大Morrey空间中的有界性质.     

面积积分及其交换子在广义加权Morrey空间上的有界性

研究含有参变量的面积积分及其与BMO函数构成的高阶交换子在广义加权Morrey空间上的估计,利用函数的局部加权估计,证明了面积积分及其高阶交换子在广义加权Morrey空间上是有界算子.这些结果改进和丰富了一些已有的研究结论.     

一些函数空间上带Dini核的Calderón-Zygmund算子的交换子（英文）

本文主要建立了带Dini核的Calderón-Zygmund算子与加权Lipschitz函数生成的交换子在加权Lebesgue空间以及加权广义Morrey空间上的有界性.进一步,给出了带Dini核的奇异积分算子在加权中心Morrey空间上的加权λ-中心BMO估计.     

Marcinkiewicz积分交换子在加权Morrey空间上的有界性

Marcinkiewicz积分是分析中的一类被广泛研究的重要算子.利用Marcinkiewicz积分算子μΩ与Lipschitz函数b生成的交换子μΩ,b在加权L~p空间上的有界性,研究了它在加权Morrey空间上的有界性.     

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.     

p-进中心函数空间及奇异积分算子

引入了几类p-中心函数空间,包括p进A~q和B~q空间、p进λ-中心BMO空间以及p-进中心Morrey空间,得到了p-进A~q空间与B~q空间的对偶性、p-进λ-中心BMO空间和中心Morrey空间的特征,研究了这些空间与加权p-进Lebesgue空间之间的关系.另外,还建立了一类奇异积分算子在p-进中心Morrey空间中的有界性,更进一步,得到了这类算子交换子在p-进中心Morrey空间中的λ-中心BMO估计.     

单边算子有界性和KdV型色散方程的适定性研究

数学和物理中许多重要问题均可归结为算子在某些函数空间中的有界性质.奇异积分算子有界性质的研究是调和分析理论的核心课题之一,由此发展起来的各种方法和技巧已广泛应用于偏微分方程的研究.借助奇异积分算子在Lebesgue空间或Morrey型空间中建立的时空估计和半群理论,可以得到非线性色散方程在低阶Sobolev空间中Cauchy问题的适定性.本文首次定义一类单边振荡奇异积分算子并研究该类算子的经典加权有界性质.受经典交换子刻画理论的启发,本文首次引入Morrey空间的交换子刻画理论.利用不同于常规极大函数的方法得到两类象征函数在Morrey空间中的交换子刻画.以上结果为偏微分方程的研究提供了新的工具.最后,结合能量方法和数论知识,本文解决几类KdV型色散方程的适定性问题.     

消失广义加权Morrey空间上的分数次积分算子(英文)

本文主要研究了带粗糙核的分数次积分算子及其与BMO函数生成的交换子在消失广义加权Morrey空间上的有界性.     

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．     

加权Hardy算子及其交换子在广义Morrey空间上的有界性

讨论了加权Hardy算子,Cesàro算子及它们与BMO函数生成的交换子的有界性.在假设ω(r)满足一类条件时,得到了这些算子及它们的交换子在广义Morrey空间上有界,且证明了这类条件是必要的.     

Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces

This paper is devoted to investigating the bounded behaviors of the oscillation and variation operators for Calderón-Zygmund singular integrals and the corresponding commutators on the weighted Morrey spaces. We establish several criterions of boundedness, which are applied to obtain the corresponding bounds for the oscillation and variation operators of Hilbert transform, Hermitian Riesz transform and their commutators with BMO functions, or Lipschitz functions on weighted Morrey spaces.     

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 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.     

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.     

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.     

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.     

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.     

关于Calderón-Zygmund 算子在加权Morrey 空间上的一些交换子估计

设T 是一个Calderón-Zygmund 奇异积分算子. 本文将采用统一的Sharp 极大函数估计的方法来证明当权函数w 满足一定条件时, 交换子[b, T] 在加权Morrey 空间L^p,k(w) 上的有界性质, 其中符号b 属于加权BMO 空间、Lipschitz 空间和加权Lipschitz 空间.     

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.