Complex symmetric difference of the weighted composition operators on weighted Bergman space of the half-plane

Zhi-jie Jiang; Zhi-jie Jiang

doi:10.3934/math.2024352

AIMS Mathematics

2024, Volume 9, Issue 3: 7253-7272. doi: 10.3934/math.2024352

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Complex symmetric difference of the weighted composition operators on weighted Bergman space of the half-plane

Zhi-jie Jiang ^{1,2
,
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1.
School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, China
2.
South Sichuan Center for Applied Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, China

Received: 26 November 2023 Revised: 06 February 2024 Accepted: 08 February 2024 Published: 20 February 2024
MSC : Primary 47B38; Secondary 47B33, 47B37, 30H05

The main goal of this paper was to completely characterize complex symmetric difference of the weighted composition operators induced by three type symbols on weighted Bergman space of the right half-plane with the conjugations $ \mathcal{J}f(z) = \overline{f(\bar{z})} $, $ \mathcal{J}_sf(z) = \overline{f(\bar{z}+is)} $, and $ \mathcal{J}_*f(z) = \frac{1}{z^{{\alpha}+2}}\overline{f(\frac{1}{\bar{z}})} $. The special phenomenon that we focus on is that the difference is complex symmetric on weighted Bergman spaces of the half-plane with the related conjugation if and only if each weighted composition operator is complex symmetric.
Citation: Zhi-jie Jiang. Complex symmetric difference of the weighted composition operators on weighted Bergman space of the half-plane[J]. AIMS Mathematics, 2024, 9(3): 7253-7272. doi: 10.3934/math.2024352

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Abstract

The main goal of this paper was to completely characterize complex symmetric difference of the weighted composition operators induced by three type symbols on weighted Bergman space of the right half-plane with the conjugations $ \mathcal{J}f(z) = \overline{f(\bar{z})} $, $ \mathcal{J}_sf(z) = \overline{f(\bar{z}+is)} $, and $ \mathcal{J}_*f(z) = \frac{1}{z^{{\alpha}+2}}\overline{f(\frac{1}{\bar{z}})} $. The special phenomenon that we focus on is that the difference is complex symmetric on weighted Bergman spaces of the half-plane with the related conjugation if and only if each weighted composition operator is complex symmetric.

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