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Research Article | Open Access

Commuting Toeplitz operators and H-Toeplitz operators on Bergman space

School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, Dalian, Liaoning, 116025, China
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Abstract

In this paper, we consider the H-Toeplitz and Toeplitz operators acting on the Bergman space. First, we describe the characterizations of commutativity of two H-Toeplitz operators with certain harmonic symbols. For the general case, it seems very hard. As an extension to the study of Toeplitz operators on the Bergman space, we present the necessary and sufficient conditions of the commutativity of the H-Toeplitz operator and the Toeplitz operator with non-harmonic symbols.

Keywords

H-Toeplitz operatorsToeplitz operatorsBergman space
CLC number: 47B35, 47B38

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 2530-2548
DOI: 10.3934/math.2024125

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Cite this article:
Ding Q. Commuting Toeplitz operators and H-Toeplitz operators on Bergman space. AIMS Mathematics, 2024, 9(1): 2530-2548. https://doi.org/10.3934/math.2024125

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Received: 30 October 2023
Revised: 02 December 2023
Accepted: 06 December 2023
Published: 15 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)