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Research Article | Open Access

Weighted composition operators on α-Bloch-Orlicz spaces over the unit polydisc

Fuya Hu1, Chengshi Huang2, Zhijie Jiang3,4( )
School of Mathematics and Information Sciences, Neijiang Normal University, Neijiang 641100, China
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China
South Sichuan Center for Applied Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China
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Abstract

Let U n be the unit polydisc in the complex vector space C n . We defined the α-Bloch-Orlicz space on U n by using Young's function and showed that its norm is equivalent with a special μ-Bloch space. We also characterized the boundedness and compactness of the weighted composition operator on α-Bloch-Orlicz space. Our results generalized the corresponding results on the unit disk.

Keywords

weighted composition operatorboundednesscompactnessα-Bloch-Orlicz spacepolydisc
CLC number: 47B33, 47B37, 47B38

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 3672-3690
DOI: 10.3934/math.2025170

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Cite this article:
Hu F, Huang C, Jiang Z. Weighted composition operators on α-Bloch-Orlicz spaces over the unit polydisc. AIMS Mathematics, 2025, 10(2): 3672-3690. https://doi.org/10.3934/math.2025170

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Received: 30 December 2024
Revised: 15 February 2025
Accepted: 20 February 2025
Published: 15 February 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)