Hardy空间上复合算子的角导数和紧致性

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Operator Theory Pub Date : 2019-07-28 DOI:10.7900/JOT.2018APR18.2196

Dimitrios Betsakos

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引用次数: 1

摘要

设Do是单位圆盘的单连通子域，a是Do的紧致子集。设φ是Do\a的泛覆盖映射。我们证明了复合算子Cφ在Hardy空间H上是紧致的，当且仅当φ在单位圆的任何点上都不具有角导数。这个结果推广了M.M.Jones的一个定理。

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Angular derivatives and compactness of composition operators on Hardy spaces

Let Do be a simply connected subdomain of the unit disk and A be a compact subset of Do. Let φ be a universal covering map for Do \ A. We prove that the composition operator Cφ is compact on the Hardy space H if and only if φ does not have an angular derivative at any point of the unit circle. This result extends a theorem of M.M. Jones.

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来源期刊

Journal of Operator Theory 数学-数学

CiteScore

1.30

自引率

12.50%

发文量

审稿时长

12 months

期刊介绍： The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.