Product of Volterra type integral and composition operators on weighted Fock spaces

TL;DR

This paper characterizes the boundedness, compactness, and Schatten class membership of product operators involving Volterra type integrals and compositions on weighted Fock spaces, using Berezin type transforms.

Contribution

It provides a comprehensive characterization of these operators' properties on weighted Fock spaces, extending existing theory with new integral transform criteria.

Findings

Operators are bounded and compact under specific Berezin transform conditions

Norms and essential norms are estimated via integral transforms

Results apply to weighted composition operators on Fock spaces

Abstract

We characterize the bounded, compact, and Schatten class product of Volterra type integral and composition operators acting between weighted Fock spaces. Our results are expressed in terms of certain Berezin type integral transforms on the complex plane $\CC$. We also estimate the norms and essential norms of these operators in terms of the integral transforms. All our results are valid for weighted composition operators when acting between the class of weighted Fock spaces considered.