Compactness of Composition Operators on the Bergman Space of the Bidisc

被引：0

作者：

Clos, Timothy G. ^{[1
]}

Cuckovic, Zeljko ^{[2
]}

Sahutoglu, Sonmez ^{[2
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Univ Toledo, Dept Math & Stat, Toledo, OH 43606 USA

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2025年 / 97卷 / 03期

关键词：

Composition operator; bidisc; compact; Bergman space; WEIGHTED COMPOSITION OPERATORS; ESSENTIAL NORMS; CONVEX DOMAINS; HARDY;

D O I：

10.1007/s00020-025-02808-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} be a holomorphic self-map of the bidisc that is Lipschitz on the closure. We show that the composition operator C phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{\varphi }$$\end{document} is compact on the Bergman space if and only if phi(D2<overline>)boolean AND T2=& empty;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi (\overline{\mathbb {D}<^>2})\cap \mathbb {T}<^>2=\emptyset $$\end{document} and phi(D2<overline>\T2)boolean AND bD2=& empty;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi (\overline{\mathbb {D}<^>2}\setminus \mathbb {T}<^>2) \cap b\mathbb {D}<^>2=\emptyset $$\end{document}. In the last section of the paper, we prove a result on C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>2$$\end{document}-smooth bounded pseudoconvex domains in Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}<^>{n}$$\end{document}.

引用

页数：13

共 23 条

[11] Composition operators on the polydisc induced by smooth symbols [J].