Weighted Composition Operators from Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Unit Ball in C-n

摘要

Let X be a Banach space of holomorphic functions on the unit ball B-n in C-n whose point-evaluation functionals are bounded. In this work, we characterize the bounded weighted composition operators from X into a weighted-type Banach space H-mu(infinity)(B-n), where the weight mu is an arbitrary positive continuous function on B-n. We determine the norm of such operators in terms of the norm of the point-evaluation functionals. Under some restrictions on X, we characterize the compact weighted composition operators mapping X into H-mu(infinity)(B-n). Under an alternative set of conditions, we provide essential norm estimates. We apply our results to the cases when X is the Hardy space H-p(B-n), the weighted Bergman space A(p)(alpha)(B-n) for alpha > -1 and 1 <= p < infinity, the Bloch space B and the little Bloch space B-0. In all these cases we obtain precise formulas of the essential norm.