R^n与非紧对称空间上的支撑定理

复对称算子的闭包：紧算子与加权移位

On the closure of the complex symmetric operators: compact operators and weighted shifts

研究了可分无限维复希尔伯特空间上所有复对称算子的集合$CSO$的闭包$\bar{CSO}$。除此之外，我们证明了$\bar{CSO}$中的每个紧算子都是复对称的。利用角谷的一个构造作为动机，我们还描述了$\bar{CSO} \backslash CSO$中加权移位的许多性质。特别是，我们表明，加权移位，表现出一种近似的自相似性属于$\bar{CSO}\backslash CSO$。作为我们处理加权移位的副产品，我们解释了几种方法，我们的结果在紧算子是最佳的。

整数的对称紧化与空间 $C_p(X)$ 的可分商空间

Symmetric compactifications of the integers and separable quotients of spaces $C_p(X)$

本文研究整数离散空间的对称紧化，将其与C_p(X)的可分商问题及Josefson--Nissenzweig序列关联，并归结到完全非对称紧化情形，为C(K)的Grothendieck性质提供新视角。

Universally symmetric norming operators are compact

We study a specific family of symmetric norms on the algebra $\mathcal B(\mathcal H)$ of operators on a separable infinite-dimensional Hilbert space. With respect to each symmetric norm in this family the identity operator fails to attain its norm. Using this, we generalize one of the main results from \cite{SP}; the hypothesis is relaxed, and consequently, the family of symmetric norms for which the result holds is extended. We introduce and study the concepts of "universally symmetric norming operators" and "universally absolutely symmetric norming operators" on a separable Hilbert space. Th…

径向对称函数的紧致Sobolev嵌入

Compact Sobolev embeddings of radially symmetric functions

本文研究了径向对称函数在不同空间中的Sobolev嵌入紧致性，提出了新的技术并给出了加权情况下的最优目标空间。

Riesz transforms on compact Riemannian symmetric spaces of rank one

In this paper we prove mixed norm estimates for Riesz transforms related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. These operators are closely related to the Riesz transforms for Jacobi polynomials expansions. The key point is to obtain sharp estimates for the kernel of the Jacobi--Riesz transforms with uniform control on the parameters, together with an adaptation of Rubio de Francia's extrapolation theorem. The latter results are of independent interest.

内部一致区域上的Dirichlet热核：局部结果、紧区域和非对称形式

The Dirichlet heat kernel in inner uniform domains: local results, compact domains and non-symmetric forms

本文在某些（可能是非对称的）类似于Dirichlet型的双线性型的上下文中，给出了内部一致区域（包括有界内部一致区域）中Dirichlet热核的精确估计.例如，本文的结果适用于$\mathbb R^n$中的一致椭圆型散度型算子的Dirichlet热核，该算子具有对称的二阶部分和内部一致区域中的有界可测系数.结果适用于任何凸区域，任何凸区域的补充，以及更奇特的例子，如内部和外部的雪花。