Compact linear combination of composition operators on Bergman spaces

Boo Rim Choe; Hyungwoon Koo; Maofa Wang

doi:10.1016/j.jfa.2019.108393

Compact linear combination of composition operators on Bergman spaces

Boo Rim Choe, Hyungwoon Koo, Maofa Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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-Carathéodory type and the other is a measure theoretic characterization of Carleson type. Our approach is completely different from what has been known so far.

Original language	English
Article number	108393
Journal	Journal of Functional Analysis
Volume	278
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2019.108393
Publication status	Published - 2020 Mar 15

Keywords

Compact operator
Composition operator
Linear combination
Weighted Bergman space

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2019.108393

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title = "Compact linear combination of composition operators on Bergman spaces",

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-Carath{\'e}odory type and the other is a measure theoretic characterization of Carleson type. Our approach is completely different from what has been known so far.",

keywords = "Compact operator, Composition operator, Linear combination, Weighted Bergman space",

author = "Choe, {Boo Rim} and Hyungwoon Koo and Maofa Wang",

note = "Funding Information: B.R. Choe was supported by NRF(2018R1D1A1B07041183) of Korea, H. Koo was supported by NRF(2017R1A2B2002515) of Korea and NSFC(11771340; 11431011) of China, and M. Wang was supported by NSFC(11771340; 11431011) of China. Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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doi = "10.1016/j.jfa.2019.108393",

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AU - Choe, Boo Rim

AU - Koo, Hyungwoon

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PY - 2020/3/15

Y1 - 2020/3/15

N2 - 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-Carathéodory type and the other is a measure theoretic characterization of Carleson type. Our approach is completely different from what has been known so far.

AB - 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-Carathéodory type and the other is a measure theoretic characterization of Carleson type. Our approach is completely different from what has been known so far.

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KW - Linear combination

KW - Weighted Bergman space

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JO - Journal of Functional Analysis

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Compact linear combination of composition operators on Bergman spaces

Abstract

Keywords

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