Abstract
Let ϕ be an entire self-map of Cn, and let u be an entire function on Cn. A weighted composition operator induced by ϕ with weight u is given by (uCϕf)(z)=u(z)f(ϕ(z)) for z in Cn and f is an entire function on Cn. In this paper, we study weighted composition operators acting between two large weighted Fock spaces Fωp and Fωq. We characterize the bounded, compact and Schatten class membership operators uCϕ acting from Fωp to Fωq when 0<p≤∞ and 0<q<∞. Our results use certain integral transforms that generalize the usual Berezin transform.
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