首页|Composition operators on weighted Bergman spaces induced by doubling weights
Composition operators on weighted Bergman spaces induced by doubling weights
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Given a doubling weight ω on the unit disk D,let Apω be the space of all the holomorphic functions f,where‖f‖Aωp:=(∫D|f(z)|pω(z)dA(z)1/p＜∞.We completely characterize the topological connectedness of the set of composition operators on Aωp.As an application,we construct an interesting example which reveals that two composition operators on Aαp 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 Aωp in three terms:a Julia-Carathéodory-type function-theoretic characterization,a power-type characterization,and a Carleson-type measure-theoretic characterization.
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