Weighted composition operators on $ \alpha $-Bloch-Orlicz spaces over the unit polydisc

Fuya Hu; Chengshi Huang; Zhijie Jiang; Fuya Hu; Chengshi Huang; Zhijie Jiang

doi:10.3934/math.2025170

AIMS Mathematics

2025, Volume 10, Issue 2: 3672-3690. doi: 10.3934/math.2025170

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Research article

Weighted composition operators on $ \alpha $-Bloch-Orlicz spaces over the unit polydisc

1.
School of Mathematics and Information Sciences, Neijiang Normal University, Neijiang 641100, China
2.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
3.
School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China
4.
South Sichuan Center for Applied Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China

Received: 30 December 2024 Revised: 15 February 2025 Accepted: 20 February 2025 Published: 25 February 2025
MSC : 47B33, 47B37, 47B38

Let $ {\mathbb{U}}^{n} $ be the unit polydisc in the complex vector space $ {\mathbb C}^n $. We defined the $ \alpha $-Bloch-Orlicz space on $ {\mathbb{U}}^n $ by using Young's function and showed that its norm is equivalent with a special $ \mu $-Bloch space. We also characterized the boundedness and compactness of the weighted composition operator on $ \alpha $-Bloch-Orlicz space. Our results generalized the corresponding results on the unit disk.
- weighted composition operator,
- boundedness,
- compactness,
- $ \alpha $-Bloch-Orlicz space,
- polydisc
Citation: Fuya Hu, Chengshi Huang, Zhijie Jiang. Weighted composition operators on $ \alpha $-Bloch-Orlicz spaces over the unit polydisc[J]. AIMS Mathematics, 2025, 10(2): 3672-3690. doi: 10.3934/math.2025170

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Abstract

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

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