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Compact linear combination of composition operators on Bergman spaces
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-03-01 , DOI: 10.1016/j.jfa.2019.108393
Boo Rim Choe , Hyungwoon Koo , Maofa Wang

Abstract Motivated by the question of Shapiro and Sundberg raised in 1990, study on linear combinations of composition operators has been a topic of growing interest. In this paper, we completely characterize the compactness of any finite linear combination of composition operators with general symbols on the weighted Bergman spaces in two classical terms: one is a function theoretic characterization of Julia-Caratheodory type and the other is a measure theoretic characterization of Carleson type. Our approach is completely different from what has been known so far.

中文翻译:

Bergman空间上复合算子的紧凑线性组合

摘要 受Shapiro和Sundberg于1990年提出的问题的启发,组合算子的线性组合研究成为越来越受关注的话题。在本文中,我们用两个经典术语完全刻画了加权伯格曼空间上具有一般符号的复合算子的任何有限线性组合的紧致性:一个是Julia-Caratheodory类型的函数理论刻画,另一个是卡尔森型。我们的方法与目前已知的完全不同。
更新日期:2020-03-01
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