消失平均振荡与重排的连续性

关于索伯列夫空间中函数Schwarz对称化的梯度

On the gradient of Schwarz symmetrization of functions in Sobolev spaces

设S是在定义域边界不为零的函数的Sobolev或Orlicz-索伯列夫空间.给出了S中非负函数的球面重排（Schwartz对称化）仍属于S的充分条件.这些结果是通过相关的等周不等式得到的，并在一定程度上推广了一个著名的Polya-Szego定理.我们还证明了任意函数在S中的重排是局部的。

A Gleason-Kahane-Żelazko theorem for the Dirichlet space

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a characterization of weighted composition operators on the Dirichlet space as being exactly those linear maps that send nowhere-vanishing functions to nowhere-vanishing functions. We also investigate possible extensions to weighted Dirichlet spaces with superharmonic weights. As part of our investigation, we are led to determine which of these spaces contain functio…

关于光滑化重排的 Pólya-Szegő 不等式

The Pólya-Szegő inequality for smoothing rearrangements

本文证明适用于所有光滑化重排的一般 Pólya-Szegő 不等式，涵盖多类函数并建立各向异性版本，将既有基本形式统一于同一框架。

The Shearlet Transform and Lizorkin Spaces

We prove a continuity result for the shearlet transform when restricted to the space of smooth and rapidly decreasing functions with all vanishing moments. We define the dual shearlet transform, called here the shearlet synthesis operator, and we prove its continuity on the space of smooth and rapidly decreasing functions over $\mathbb{R}^2\times\mathbb{R}\times\mathbb{R}^\times$. Then, we use these continuity results to extend the shearlet transform to the space of Lizorkin distributions, and we prove its consistency with the classical definition for test functions.

Strict continuity of the transition semigroup for the solution of a well-posed martingale problem

In this note we connect the notion of solutions of a martingale problem to the notion of a strongly continuous and locally equi-continuous semigroup on the space of bounded continuous functions equipped with the strict topology. This extends the classical connection of semigroups to Markov processes that was used successfully in the context of compact spaces to the context of Polish spaces. In addition, we consider the context of locally compact spaces and show how the transition semigroup on the space of functions vanishing at infinity can be extended to the space of bounded continuous functi…

有界对称域上的一致连续性与量子化

Uniform Continuity and Quantization on Bounded Symmetric Domains

考虑有界对称域$Ω\subset \mathbb{C}^n$上的Toeplitz算子$T_f^λ$，符号为$f$，作用在标准加权Bergman空间上.这里的$λ> genus-1$是权重参数。将经典的渐近半换位子关系$\lim_{λ\rightarrow \infty} \big{\|}T_f^λ T_g^λ -T_{fg}^λ \big{\|}=0$与$f,g \in C(\overline{\mathbb{B}^n})$（其中$Ω=\mathbb{B}^n$表示复单位球）推广到更大类的有界和无界算子符号函数以及更一般的域.我们处理的算子符号一般既不是连续的$Ω$（第4节）内，也不承认一个连续的延伸到边界（第3和4节）。令$β$表示$Ω$上的Bergman度量距离函数。证明了在$Ω$上所有$β$ -一致连续函数的空间${\rm UC}(Ω)$中，$f$和$g$的半换位子关系仍然成立.注意，这个空间也包含无界函数。在复杂的单位球$Ω=\mathbb{B}^n \subset \mathbb{C}^n$的情况下，我们表明，半换向器关系成立的有界符号在${\rm VMO}(\mathbb{B}^n)$，其中消失的振荡内$\mathbb{B}^n$测量相对于$β$。同时，半换位子关系对一般有界可测符号失效。我们构造了一个相应的反例，使用振荡符号是连续的$Ω$中的一个单一的点之外。

紧致域上BMO函数的尖锐体积型界及其应用

Sharp Volume-Based Bounds for BMO Functions on Compact Domains and Applications

本文为紧支撑BMO函数建立以支撑集Lebesgue测度替代直径的尖锐局部$L^r$界，并应用于几何坍缩、薛定谔算子谱界及奇异积分解耦。