Weighted composition operators between large Fock spaces in several complex variables

Let phi be an entire self-map of C-n, and let u be an entire function on C-n. A weighted composition operator induced by phi with weight u is given by (uC phi f)(z) = u(z) f (phi(z)) for z in C-n and f is an entire function on C-n. In this paper, we study weighted composition operators acting between two large weighted Fock spaces F-w(p) and F-w(q). We characterize the bounded, compact and Schatten class membership operators uC(phi), acting from F-w(p) to F-w(q) when 0 < p <= infinity and 0 < q < infinity. Our results use certain integral transforms that generalize the usual Berezin transform. (C) 2019 Published by Elsevier Inc.