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

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 D-n into weighted-type Banach spaces of holomorphic functions on D-n. 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.