Trace class criteria for Toeplitz and composition operators on small Bergman spaces

被引：33

作者：

Angel Pelaez, Jose ^{[1
]}

Rattya, Jouni ^{[2
]}

机构：

[1] Univ Malaga, Dept Anal Matemat, Campus Teatinos, E-29071 Malaga, Spain

[2] Univ Eastern Finland, POB 111, Joensuu 80101, Finland

来源：

ADVANCES IN MATHEMATICS | 2016年 / 293卷

基金：

芬兰科学院;

关键词：

Trace class; Toeplitz operator; Composition operator; Bergman space; Essential norm; Angular derivative; ESSENTIAL NORM;

D O I：

10.1016/j.aim.2016.02.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize the Schatten class Toeplitz operators induced by a positive Borel measure on the unit disc and the reproducing kernel of the Bergman space A(w)(2), where w is a radial weight satisfying the doubling property integral(1)(r) w(s) ds <= C integral(1)(1+r/2)w(s) ds. By using this, we describe the Schatten class composition operators. We also discuss basic properties of composition operators acting from A(w)(p) to A(v)(q). (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：606 / 643

页数：38

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