文献类型：期刊文献

英文题名：Composition operators on distinct Bergman spaces over planar domains

作者：Li, Shan[1];Huang, Hansong[1]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2020

卷号：26

起止页码：1184

外文期刊名：NEW YORK JOURNAL OF MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000579353400001)】；

基金：This work is partially supported by NSFC (12071134, 11471113). We thank the referee for his/her suggestions to improve the paper.

语种：英文

外文关键词：Bergman spaces; composition operators; domains of C-2-boundary

摘要：In this paper, we will consider composition operators defined between distinct Bergman spaces over planar domains. The smoothness on boundary of the domains plays an important role in our study. On one hand, an essential extension of Littlewood's Subordination Principle is obtained. Precisely, for each holomorphic map that is defined between bounded domains of smooth boundaries, the associated composition operator is always bounded. This essentially depends on a "standard decomposition" of holomorphic functions over a classical domain, bounded by finitely many disjoint circles. On the other hand, the situation becomes complex if domains with cusp boundary points are concerned, and there exists a link between the boundary behavior of the function symbol and the boundedness of the associated composition operator, where a detailed discussion is presented. Finally, we give estimates of norms for some classes of such composition operators. A deep interplay of function theory, geometry, and operator theory is revealed.