Composition operators on weighted Bergman spaces induced by doubling weights  

作　　者：Xin Guo Maofa Wang 

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan,430072,China

出　　处：《Science China Mathematics》2024年第7期1571-1598,共28页中国科学（数学）（英文版）

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

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 space.In 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.

关 键 词：composition operator linear combination linearly connected weighted Bergman space doubling weight 

分 类 号：O177[理学—数学]