Weighted Composition Operators from H∞ to α,m-Bloch Space on Cartan-Hartogs Domain of the First Type

Abstract

Let YI be nonhomogeneous Cartan-Hartogs domain of the first type, ϕ a holomorphic self-map, and ψ a fixed holomorphic function on YI. We study the weighted composition operator ψCϕf=ψf∘ϕ for a function f holomorphic on YI. Our main results generalize both cases of the unit ploydisc and the unit ball obtained by Li and Stević (Li 2007 and Li 2008). Firstly, we obtain two crucial inequalities on YI; furthermore, the boundedness and compactness of operator ψCϕ from the space H∞ of all bounded holomorphic functions to the α,m-Bloch space Bα,m on YI are investigated.