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.     

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.     

Two weight commutators in the Dirichlet and Neumann Laplacian settings

In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian ${\mathrm{\Delta }}_{N_{+}}$ on the upper half space ${\mathbb{R}}_{+}^n$ and the reflection Neumann Laplacian ${\mathrm{\Delta }}_N$ on ${\mathbb{R}}^n$ with respect to the weights associated to ${\mathrm{\Delta }}_{N_{+}}$ and ${\mathrm{\Delta }}_N$ respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to ${\mathrm{\Delta }}_N$ is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on ${\mathbb{R}}^n$ and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt $A^p$ weights with $p\in (1,2]$ while the previously known related results cover only $p\in (1,\frac{n+1}{n}]$. We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian ${\mathrm{\Delta }}_{D_{+}}$ on ${\mathbb{R}}_{+}^n$.     

Derivative Estimates of Semigroups and Riesz Transforms on Vector Bundles

We use versions of Bismut type derivative formulas obtained by Driver and Thalmaier [9], to prove derivative estimates for various heat semigroups on Riemannian vector bundles. As an application, the weak (1,1) property for a class of Riesz transforms on a vector bundle is established. Some concrete examples of vector bundles (e.g., differential forms) are considered to illustrate the results.     

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。     

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。     

Self-similar Solutions for a Transport Equation with Non-local Flux

The authors construct self-similar solutions for an N-dimensional transport equation, where the velocity is given by the Riezs transform. These solutions imply non-uniqueness of weak solution. In addition, self-similar solution for a one-dimensional conservative equation involving the Hilbert transform is obtained.     

由schr(o)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Lp空间的有界性.