Commuting Toeplitz operators and H-Toeplitz operators on Bergman space

Qian Ding; Qian Ding

doi:10.3934/math.2024125

AIMS Mathematics

2024, Volume 9, Issue 1: 2530-2548. doi: 10.3934/math.2024125

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Research article

Commuting Toeplitz operators and H-Toeplitz operators on Bergman space

Qian Ding ^,

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

Received: 30 October 2023 Revised: 02 December 2023 Accepted: 06 December 2023 Published: 25 December 2023
MSC : 47B35, 47B38

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.
- H-Toeplitz operators,
- Toeplitz operators,
- Bergman space
Citation: Qian Ding. Commuting Toeplitz operators and H-Toeplitz operators on Bergman space[J]. AIMS Mathematics, 2024, 9(1): 2530-2548. doi: 10.3934/math.2024125

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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.

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