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Research Article | Open Access

Dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
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Abstract

This paper aimed to give some partial answers to the zero-product problem and commutativity problem concerning dual Toeplitz operators with nonharmonic symbols on the orthogonal complement of the harmonic Bergman space. Using the symbol map, we described the necessary condition for Sφ1Sφ2⋯SφN=0 with radial symbols. Furthermore, we established the sufficient and necessary conditions for SφSψ=SψSφ with φ(z)=azp1z¯q1+bzp2z¯q2 and ψ(z)=zsz¯t.

Keywords

dual Toeplitz operatorharmonic Bergman spacezero-product problemcommutativity
CLC number: 47B35

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 25413-25437
DOI: 10.3934/math.20241241

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Liu L. Dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space. AIMS Mathematics, 2024, 9(9): 25413-25437. https://doi.org/10.3934/math.20241241

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Received: 26 June 2024
Revised: 14 August 2024
Accepted: 23 August 2024
Published: 15 September 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)