J. Korean Math. Soc. 2021; 58(4): 799-817
Online first article May 31, 2021 Printed July 1, 2021
https://doi.org/10.4134/JKMS.j190722
Copyright © The Korean Mathematical Society.
Hang Zhou, Ze-Hua Zhou
Tianjin Chengjian University; Tianjin University
In this paper, we investigate the normal and complex symmetric weighted composition operators $W_{\psi,\varphi}$ on the Hardy space $H^2(\mathbb{D})$. Firstly, we give the explicit conditions of weighted composition operators to be normal and complex symmetric with respect to conjugations $\mathcal{C}_1$ and $\mathcal{C}_2$ on $H^2(\mathbb{D})$, respectively. Moreover, we particularly investigate the weighted composition operators $W_{\psi,\varphi}$ on $H^2(\mathbb{D})$ which are normal and complex symmetric with respect to conjugations $\mathcal{J}$, $\mathcal{C}_1$ and $\mathcal{C}_2$, respectively, when $\varphi$ has an interior fixed point, $\varphi$ is of hyperbolic type or parabolic type.
Keywords: Normality, complex symmetric, weighted composition operators, automorphism, Hardy space
MSC numbers: Primary 47B33; Secondary 47B32, 47A05
Supported by: The work was supported in part by the National Natural Science Foundation of China (Grant Nos.11771323;11801402).
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