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.
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页码：211 / 229
页数：19
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