Composition Operators on the Bergman Space with Quasiconformal Symbols

Xiang Fang; Kunyu Guo; Zipeng Wang

doi:10.1007/s12220-022-01172-y

Composition Operators on the Bergman Space with Quasiconformal Symbols

Xiang Fang, Kunyu Guo, Zipeng Wang^*

^*Corresponding author for this work

Department of Applied Mathematics

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

Abstract

This paper introduces and studies composition operators on the Bergman space with quasiconformal symbols. We first characterize the boundedness of the norms. Then we discuss operator-theoretic issues including compactness characterization, essential norms, Schatten class membership, and conditions for closed ranges.

Original language	English
Article number	125
Journal	Journal of Geometric Analysis
Volume	33
Issue number	4
DOIs	https://doi.org/10.1007/s12220-022-01172-y
State	Published - Apr 2023

Keywords

Bergman space
Carleson box
Composition operator
Quasiconformal mapping

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title = "Composition Operators on the Bergman Space with Quasiconformal Symbols",

abstract = "This paper introduces and studies composition operators on the Bergman space with quasiconformal symbols. We first characterize the boundedness of the norms. Then we discuss operator-theoretic issues including compactness characterization, essential norms, Schatten class membership, and conditions for closed ranges.",

keywords = "Bergman space, Carleson box, Composition operator, Quasiconformal mapping",

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AU - Guo, Kunyu

AU - Wang, Zipeng

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N2 - This paper introduces and studies composition operators on the Bergman space with quasiconformal symbols. We first characterize the boundedness of the norms. Then we discuss operator-theoretic issues including compactness characterization, essential norms, Schatten class membership, and conditions for closed ranges.

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KW - Carleson box

KW - Composition operator

KW - Quasiconformal mapping

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Composition Operators on the Bergman Space with Quasiconformal Symbols

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Keywords

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