# WEIGHTED COMPOSITION OPERATORS ON BERS-TYPE SPACES OF LOO-KENG HUA DOMAINS

• Jiang, Zhi-jie (School of Mathematics and Statistics Sichuan University of Science and Engineering) ;
• Li, Zuo-an (School of Mathematics and Statistics Sichuan University of Science and Engineering)
• Accepted : 2020.01.17
• Published : 2020.05.31

#### Abstract

Let HEI, HEII, HEIII and HEIV be the first, second, third and fourth type Loo-Keng Hua domain respectively, 𝜑 a holomorphic self-map of HEI, HEII, HEIII, or HEIV and u ∈ H(𝓜) the space of all holomorphic functions on 𝓜 ∈ {HEI, HEII, HEIII, HEIV}. In this paper, motivated by the well known Hua's matrix inequality, first some inequalities for the points in the Bers-type spaces of the Loo-Keng Hua domains are obtained, and then the boundedness and compactness of the weighted composition operators W𝜑,u : f ↦ u · f ◦ 𝜑 on Bers-type spaces of these domains are characterized.

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