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

Let Y-I be nonhomogeneous Cartan-Hartogs domain of the first type, phi a holomorphic self-map, and psi a fixed holomorphic function on Y-I. We study the weighted composition operator psi C(phi)f = psi(f circle phi) for a function f holomorphic on Y-I. Our main results generalize both cases of the unit ploydisc and the unit ball obtained by Li and Stevic (Li 2007 and Li 2008). Firstly, we obtain two crucial inequalities on Y-I; furthermore, the boundedness and compactness of operator psi C-phi from the space H-infinity of all bounded holomorphic functions to the (alpha, m)-Bloch space B-(alpha,B-m) on Y-I are investigated.