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Research Article | Open Access

Composition operators from harmonic H ∞ space into harmonic Zygmund space

Munirah Aljuaid1, Mahmoud Ali Bakhit2( )
Department of Mathematics, Faculty of Science, Northern Border University, Arar 73222, Saudi Arabia
Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
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Abstract

This research paper sought to characterize the boundedness and compactness of composition operators from the space H ∞ of bounded harmonic mappings into harmonic Zygmund space Z H , on the open unit disk. Furthermore, we obtain an estimate of the essential norms of such an operator. These results extends the similar results that were proven for composition operators on analytic function spaces.

Keywords

harmonic Zygmund spaceharmonic H∞ spacecomposition operatorsessential norm
CLC number: 30H30, 31A05

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 23087-23107
DOI: 10.3934/math.20231175

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Cite this article:
Aljuaid M, Bakhit MA. Composition operators from harmonic H ∞ space into harmonic Zygmund space. AIMS Mathematics, 2023, 8(10): 23087-23107. https://doi.org/10.3934/math.20231175

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Received: 09 April 2023
Revised: 26 June 2023
Accepted: 14 July 2023
Published: 15 October 2023
©2023 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)