The Generalized Volterra Integral Operator and Toeplitz Operator on Weighted Bergman Spaces

被引：0
作者：
Juntao Du
Songxiao Li
Dan Qu
机构：
[1] Guangdong University of Petrochemical Technology,Department of mathematics
[2] Shantou University,Department of Mathematics
[3] Macau University of Science and Technology,Faculty of Innovation Engineering
来源：
Mediterranean Journal of Mathematics | 2022年 / 19卷
关键词：
Bergman space; Volterra integral operator; Toeplitz operator; 30H20; 47B38; 47B35;
D O I：
暂无
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学科分类号：
摘要：
We study the boundedness and compactness of the generalized Volterra integral operator on weighted Bergman spaces with doubling weights on the unit disc. A generalized Toeplitz operator is defined and the boundedness, compactness and Schatten class membership of this operator are investigated on the Hilbert weighted Bergman space. As an application, Schatten class membership of generalized Volterra integral operators are also characterized. Finally, we also get the characterizations of Schatten class membership of generalized Toeplitz operator and generalized Volterra integral operators on the Hardy space H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^2$$\end{document}.
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