Weighted composition operators between Fock spaces in several variables

TL;DR

This paper establishes criteria for when weighted composition operators are bounded or compact between Fock spaces in multiple complex variables, and provides estimates for their essential norms.

Contribution

It introduces new criteria for boundedness and compactness of weighted composition operators between multivariable Fock spaces, along with essential norm estimates.

Findings

Criteria for boundedness of operators

Criteria for compactness of operators

Essential norm estimates

Abstract

We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.