Big Hankel operators on vector-valued Fock spaces in $\C^d$

TL;DR

This paper characterizes the boundedness, compactness, and Schatten class membership of big Hankel operators on vector-valued Fock spaces with radial weights in multiple complex variables.

Contribution

It provides comprehensive criteria for these properties, extending the understanding of Hankel operators in the context of vector-valued Fock spaces.

Findings

Characterization of boundedness conditions

Criteria for compactness of Hankel operators

Conditions for Schatten class membership

Abstract

We study big Hankel operators acting on vector-valued Fock spaces with radial weights in $\C^d$. We provide complete characterizations for the boundedness, compactness and Schatten class membership of such operators.