Composition operators on weighted Bergman spaces induced by doubling weights

作     者：Xin Guo Maofa Wang 

作者机构：School of Mathematics and StatisticsWuhan UniversityWuhan430072China 

出 版 物：《Science China Mathematics》 (中国科学（数学）（英文版）)

年 卷 期：2024年第67卷第7期

页      面：1571-1598页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 12101467 and 12171373) 

主　　题：composition operator linear combination linearly connected weighted Bergman space doubling weight 

摘      要：Given a doubling weightωon the unit disk D,let A_(ω)^(p) be the space of all the holomorphic functions f,where∥f∥A_(ω)^(p):=(∫_(D)|f(z)|_(p)ω(z)dA(z))^(1/p)∞.We completely characterize the topological connectedness of the set of composition operators on A_(ω)^(p).As an application,we construct an interesting example which reveals that two composition operators on A_(α)^(p) in the same path component may fail to have a compact difference and give a negative answer to the Shapiro-Sundberg question in the(standard)weighted Bergman *** addition,we completely describe the central compactness of any finite linear combinations of composition operators on A_(ω)^(p) in three terms:a Julia-Carathéodory-type function-theoretic characterization,a power-type characterization,and a Carleson-type measure-theoretic characterization.