文献类型：期刊文献

英文题名：ON COMPACTNESS OF COMPOSITION OPERATORS ON BERGMAN SPACES OVER PLANAR DOMAINS

作者：Chen, Yong[1];Huang, Hansong[2];Li, Shan[3]

机构：[1]Hangzhou Normal Univ, Dept Math, Hangzhou 311121, Peoples R China;[2]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[3]Jiangsu Univ Technol, Dept Math, Changzhou 213001, Jiangsu, Peoples R China

年份：2022

卷号：48

期号：2

起止页码：319

外文期刊名：HOUSTON JOURNAL OF MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001126103300007)】；

基金：Supported by NNSF of China (Grant Nos. 12071134, 11771401).

语种：英文

外文关键词：Bergman spaces; compact composition operators

摘要：In this paper we consider compact composition operators acting between Bergman spaces over planar domains. When those two domains equal the open unit disc, it is well known that any analytic selfmap of that disc induces a bounded composition operator, and that operator is compact if and only if the inducing selfmap has no finite angular derivative on the unit circle. We reformulate that condition in geometric terms and prove that it characterizes compact composition operators between Bergman spaces over planar domains if the boundaries of those domains are C-2-smooth. We give examples showing that the smoothness condition cannot be dropped. We also discuss some interesting phenomena related to domains with cusps on the boundary.