Boundedness and Compactness of Weighted Composition Operators From Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Polydisk

Abstract

In this work, we characterize the bounded and compact weighted composition operators from a large class of Banach space X of holomorphic functions on the open unit polydisk Dn into weighted-type Banach spaces of holomorphic functions on Dn. Under some restrictions on the space, we provide an approximation of the essential norm of such operators. We apply our results to the cases when X is the Hardy Hilbert space, the weighted Bergman Hilbert space, a weighted-type Dirichlet space, and the Bloch space of the polydisk.