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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)
  • Received : 2019.02.25
  • 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, �� a holomorphic self-map of HEI, HEII, HEIII, or HEIV and u ∈ H(��) the space of all holomorphic functions on �� ∈ {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 W��,u : f ↦ u · f ◦ �� on Bers-type spaces of these domains are characterized.

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