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http://dx.doi.org/10.4134/BKMS.b190220

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.3, 2020 , pp. 583-595 More about this Journal
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.
Keywords
Weighted composition operator; Hua's matrix inequality; Loo-Keng Hua domain; Bers-type space; boundedness; compactness;
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