Bochner—Riesz算子及其高阶交换子L^p有界的必要条件

通过选择适当的L^p函数并应用连续分解方法,给出了低于临界阶的Bochner—Riesz算子在L^p空间有界的新的证明,同时得到了该算子和Lipschitz函数构成的高阶交换子L^p有界性的必要条件．     

Bochner—Riesz算子交换子在加权Morrey空间上的有界性

运用了Sharp极大函数估计的方法证明了当权函数满足一定条件时,Bochner～Riesz算子与加权BMO函数生成的交换子在加权Morrey空间上的有界性．     

Continuity for Maximal Multilinear Bochner-Riesz Operators on Hardy and Herz Hardy Spaces

Let Baδ^A. be the maxiamal multilinear Bochner-Riesz operators generated by Bochner Riesz operators and D^αA∈ Lipβ（｜α｜= m）, The continuity of the operator on some Hardy and Herz type Hardy is obtained.     

极大多线性Bochner-Riesz算子Herz型估计

设BδA,*是由Bochner-Riesz算子生成的极大多线性Bochner-Riesz算子,其中DγA∈Λ.β(|γ|=m).获得这个算子及其变形在中心Campanato空间的连续性.     

极大多线性Bochner-Riesz算子Triebel-Lizorkin空间估计

设BδA,*是由Bochner-Riesz算子生成的极大多线性Bochner-Riesz算子,其中DγA∈Λ.β(γ=m).我们得到了在一定条件下,极大多线性Bochner-Riesz算子在Triebel-Lizorkin空间中的有界性.     

一般多项式有界算子的泛函表示定理

该文在圆盘代数A(D)中引入了一个数乘变换, 找到了多项式有界算子的多项式演算与Riesz函数演算之间的联系, 得到了Banach空间X上的一般多项式有界算子的泛函表示定理.     

极大多线性Bochner-Riesz算子Lipschitz型估计

设BδA,*是由Bochner-Riesz算子生成的极大多线性Bochner-Riesz算子,其中DγA∈.Λβ(|γ|=m).证明了这个算子及其变形从Lp(Rn)空间到Lipschitz空间.Λβ-n/p(Rn)上的有界性.     

实数加群上算子调和分析中F.和M.Riesz定理

设G是实数加群,B表示G上的无Order齐次Banach代数,表示B中的右平移可积算子全体.在一些合宜条件下,我们得到如下结果:(1)在中的算子关于F.Riesz和M.Riesz第一定理成立。(2)在中解析算子关于F.Riesz和M.Riesz第二定理成立。     

关于正双线性算子扩张的注记

研究了定义在Riesz空间Cartesian乘积的序理想上的正双线性算子的扩张问题,得到了该类算子关于向量格运算的表达.     

一类乘子算子在全测度集上的逼近

本文给出了研究乘子算子在全测度集上逼近的一种框架.在 Riesz 极大算子有界的条件下,确定了一类乘子算子在 Riesz 位势空间上几乎处处逼近的阶.并用于讨论广义 Bochner-Riesz 平均和 Abel-Cartwright 平均的点态逼近.     

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.     

Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces

We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator. This work was supported by Key Academic Discipline of Zhejiang Province of China and National Natural Science Foundation of China (Grant Nos. 10571014, 10631080, 10671019)     

Some weighted estimates for Littlewood-Paley functions and radial multipliers

We prove some weighted estimates for certain Littlewood-Paley operators on the weighted Hardy spaces H_w^p (0<p?1) and on the weighted L^p spaces. We also prove some weighted estimates for the Bochner-Riesz operators and the spherical means.     

Convergence of a class of means of Hp functions (0<p<1) on compact lie groups

In this paper we study the convergence of a class of means on H^p(G) (0<p<1), the means take the Bochner-Riesz means in [1], the generalized Bochner-Riesz means in [2], and the operators T^σ, in [3] as special cases. We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means. Supported by NSFC     

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.     

The Continuity of Commutators on Triebel-Lizorkin Spaces

The purpose of this paper is to study the continuity in the context of Triebel-Lizorkin spaces for some commutators related to certain convolution operators. The operators include Littlewood-Paley operator, Marcinkiewicz integral and Bochner-Riesz operator.