齐次Morrey-Herz空间上广义Riesz变换

主要研究与二阶散度型椭圆算子L相伴的Riesz变换▽L-1/2"及其与BMO(Rn)函数生成的交换子,采用对函数进行环形分解的技术和对算子转化为相应的截断算子的方法,得出它们从MKp1,qα,λ(Rn)到MKp2,qα,λ(Rn)是有界的,从而推广了以前学者的结论.     

The BMO L space and Riesz transforms associated with Schrödinger operators

Let L =△ ＋ V be a SchrSdinger operator in Rd, d ≥ 3, where the nonnegative potential V belongs to the reverse HSlder class Sd. We establish the BMOL-boundedness of Riesz transforms З/ЗxiL-1/2, and give the Fefferman-Stein type decomposition of BMOL functions.     

由Campanato型函数和与薛定谔算子相关的Riesz变换生成的Toeplitz算子的有界性

本文研究了由Campanato型函数及与Schrödinger算子相关的Riesz变换生成的Toeplitz算子的有界性.利用Sharp极大函数估计得到了Toeplitz算子Θ^b在Lebesgue空间的有界性，拓广了已有交换子的结果.     

Calderón–Zygmund Operators in the Bessel Setting for All Possible Type Indices

We show that many harmonic analysis operators in the Bessel setting,including maximal operators,Littlewood–Paley–Stein type square functions,multipliers of Laplace or Laplace–Stieltjes transform type and Riesz transforms are,or can be viewed as,Calderón–Zygmund operators for all possible values of type parameter λ in this context.This extends results existing in the literature,but being justified only for a restricted range of λ.     

非负Ricci曲率Riemann流形上的Sobolev不等式及Sobolev嵌入定理

设Ｍ是具有非负Ｒｉｃｃｉ曲率的完备Ｒｉｅｍａｎｎ流形，本文证明Ｍ上Ｓｏｂｏｌｅｖ不等式‖ｆ‖ｑ≤Ｃｎ，ｐ，ｑ（１≤Ｐ，ｑ＜∞）对一切（Ｍ）成立的充要条件是对一切ｘ∈Ｍ，Ｖｘ（ｒ）＝Ｖｏｌ（Ｂｘ（ｒ））≥且，而Ｍ上较弱的Ｓｏｂｏｌｅｖ不等式‖ｆ‖ｑ≤Ｃｎ‖Ｆ‖ｐ）（１＜ｐ＜ｑ＜∞）对一切ｆ∈Ｈ（Ｍ）成立的充要条件是，且最后，证明了Ｍ上ｓｏｂｏｌｅｖ嵌入定理，如果，则；如果则成立．     

由Schr?dinger算子定义的Riesz变换的Lp估计

本文主要讨论了当非负位势 V(x)属于某逆Holder类时,由一致椭圆算子L=-div(A(x))+V(x)所定义的 Riesz变换在 L^p空间的有界性。     

The ρ-variation of the Hermitian Riesz transform

In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps LP（R, w（x）dx） into itself when w is a weight in the Ap class for 1 〈 p 〈 ∞. For p = 1 we get weak type for the A1 class. Weighted estimated are also obtained in the extreme case p = ∞.     

一类振荡奇异积分及其局部化算子的HK_p（R~n）－有界性

记１＜Ｐ＜∞．本文考察了一类卷积型的振荡奇异积分及其局部化算子的ＨＫｐ（Ｒｎ）－有界性．     

流形上的Riesz变换

设 Ｍ为一完备 Ｒｉｅｍａｎｎ流形， Ｓｔｒｉｃｈａｒｔｚ Ｒ． Ｓ， Ｌｏｈｏｕｅ Ｎ．， Ｂａｋｒｙ Ｄ．及作者等建立了 Ｍ上 Ｒｉｅｓｚ变换Ｒ的 Ｌ~ｐ（１＜ Ｐ＜ ∞）与弱型（１，１）有界性．本文将用分析的方法对曲率非负的流形建立Ｒ的Ｌ*－有界性．     

由Schrdinger算子定义的Riesz变换的L~p估计(英文)

本文主要讨论了当非负位势 V(x)属于某逆Holder类时,由一致椭圆算子L=-div(A(x))+V(x)所定义的 Riesz变换在 L~p空间的有界性。