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Research Article | Open Access

On the commuting problem of Toeplitz operators on the harmonic Bergman space

Hasan Iqtaish, Issam Louhichi, Abdelrahman Yousef( )
Department of Mathematics and Statistics, College of Arts and Sciences, American University of Sharjah, Sharjah, UAE
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Abstract

In this paper, we provide a complete characterization of bounded Toeplitz operators T f on the harmonic Bergman space of the unit disk, where the symbol f has a polar decomposition truncated above, that commute with T z + g ¯ for a bounded analytic function g.

Keywords

harmonic Bergman spaceToeplitz operatorsMellin transform
CLC number: Primary 47B35; Secondary 47L80

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AIMS Mathematics
Volume 10 Issue 7,
July 2025
Pages 17232-17247
DOI: 10.3934/math.2025770

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Cite this article:
Iqtaish H, Louhichi I, Yousef A. On the commuting problem of Toeplitz operators on the harmonic Bergman space. AIMS Mathematics, 2025, 10(7): 17232-17247. https://doi.org/10.3934/math.2025770

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Received: 24 March 2025
Revised: 11 July 2025
Accepted: 22 July 2025
Published: 15 July 2025
©2025 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)