Sparse domination of weighted composition operators on weighted Bergman spaces

被引：2

作者：

Hu, Bingyang ^{[1
]}

Li, Songxiao ^{[2
]}

Shi, Yecheng ^{[3
]}

Wick, Brett D. ^{[4
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Univ Elect Sci & Technol China, Inst Fundamental & Frontier Sci, Chengdu 610054, Sichuan, Peoples R China

[3] Lingnan Normal Univ, Sch Math & Stat, Zhanjiang 524048, Guangdong, Peoples R China

[4] Washington Univ, Dept Math & Stat, St Louis, MO 63130 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2021年 / 280卷 / 06期

基金：

美国国家科学基金会; 澳大利亚研究理事会;

关键词：

Sparse domination; Weighted Bergman spaces; Weighted composition operators; Weighted estimates; PROJECTION;

D O I：

10.1016/j.jfa.2020.108897

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the A(2) theorem for Calderon-Zygmund operators in harmonic analysis. Using this tool from harmonic analysis, some new characterizations are given for the boundedness and compactness of weighted composition operators acting between weighted Bergman spaces in the upper half plane. Moreover, we establish a new weighted type estimate for the holomorphic Bergman-class functions, for a new class of weights, which is adapted to Sawyer-testing conditions. We also extend our results to the unit ball B in C-n. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：26

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