Volterra type and weighted composition operators on Fock spaces

TL;DR

This paper characterizes boundedness and compactness of Volterra type and weighted composition operators on Fock spaces, providing norm estimates via Berezin transforms, and extends results to weighted composition operators.

Contribution

It introduces new criteria for boundedness and compactness of these operators on Fock spaces, including norm estimates and generalizations to weighted composition operators.

Findings

Bounded and compact criteria for Volterra type operators

Norm estimates using Berezin transforms

Extension to weighted composition operators

Abstract

Bounded and compact product of Volterra type integral and composition operators acting between weighted Fock spaces are described. We also estimate the norms of these operators in terms of Berezin type integral transforms on the complex plan $\mathbb{C}$. All our results are valid for weighted composition operators acting on the class of Fock spaces considered under appropriate interpretation of the weights.