Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2021; 58(6): 1347-1365

Online first article September 17, 2021      Printed November 1, 2021

https://doi.org/10.4134/JKMS.j200689

Copyright © The Korean Mathematical Society.

Bergman type operators on some generalized Cartan-Hartogs domains

Le He, Yanyan Tang, Zhenhan Tu

Wuhan University; Henan University; Wuhan University

Abstract

For $\mu=(\mu_1,\dots,\mu_t)$ ($\mu_j>0$), $\xi=(z_1,\dots,z_t,w)\in \mathbb{C}^{n_1}\times\cdots\times \mathbb{C}^{n_t}\times \mathbb{C}^m$, define $$\Omega(\mu,t)\!=\!\big\{\xi\in\mathbb{B}_{n_1}\times\cdots\times\mathbb{B}_{n_t}\times\mathbb{C}^{m}: \|w\|^2

Keywords: Bergman type operator, generalized Cartan-Hartogs domain, weighted Bergman space

MSC numbers: 32A36, 32A07, 47B34

Supported by: This work was supported by the National Natural Science Foundation of China (No.12071354).