有限型凸域上的小指数 Schatten 类 Toeplitz 算子

中文摘要 AI 辅助

本文研究了 \\(\C^n\\) 中光滑有界有限型凸域上 Schatten \\(p\\)-类 Toeplitz 算子的刻画。一方面，通过使用离散 Kobayashi 格，我们采用概率选择方法刻画了 \\(0<p<1\\) 时的 Schatten \\(p\\)-类 Toeplitz 算子。同时，我们证明了对于 \\(p > \frac{n}{n+1}\\)，由 Kobayashi 格得到的刻画与 Berezin 变换等价。另一方面，作为应用，该准则给出了 \\(0<p<2\\) 时 Schatten \\(p\\)-类加权复合算子的几何刻画，并给出了 \\(p>\frac{2n}{n+1}\\) 时的解析刻画。我们的主要结果回答了 Xiao-Yang-Yuan 在文献 \cite{Xiao2026} 中提出的关于当 \\(0<p<2\\) 时寻找 Schatten \\(p\\)-类加权复合算子的几何或解析刻画的问题。

英文摘要

In this paper, we study the characterizations of Schatten \(p\)-class Toeplitz operators on smoothly bounded convex domains of finite type in \(\C^n\). On one hand, by using discrete Kobayashi lattice, we characterize the Schatten \(p\)-class Toeplitz operators by employing a probabilistic selection method for \(0<p<1\). At the same time, we show that the characterizations obtained by Kobayashi lattice are equivalent to the Berezin transform for \(p > \frac{n}{n+1}\). On the other hand, as an application, the criterion gives a geometric characterization for Schatten \(p\)-class weighted composition operators for \(0<p<2\) and also gives an analytic characterization for \(p>\frac{2n}{n+1}\). Our main results give an answer to the question that find a geometric or analytic characterization of the Schatten \(p\)-class weighted composition operators whenever \(0<p<2\) raised by Xiao-Yang-Yuan \cite{Xiao2026}.

发表机构

• Guizhou Normal University School of Mathematical Sciences（贵州师范大学数学科学学院）

机构由 AI 辅助整理，请以论文原文为准。