Carleson Measures and Toeplitz Operators on Small Bergman Spaces on the Ball

被引：1

作者：

Le, Van An ^{[1
,2
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M, Marseille, France

[2] Univ Quynhon, Dept Math & Stat, 170 An Duong Vuong, Quy Nhon, Vietnam

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2021年 / 71卷 / 01期

关键词：

Bergman space; Carleson measure; Toeplitz operator; Schatten classes; TRACE IDEAL CRITERIA;

D O I：

10.21136/CMJ.2020.0265-19

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Carleson measures and Toeplitz operators on the class of so-called small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip's results from the unit disk of DOUBLE-STRUCK CAPITAL C to the unit ball of DOUBLE-STRUCK CAPITAL C-n. We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten p classes membership of Toeplitz operators for 1 < p < infinity.

引用

页码：211 / 229

页数：19

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