Absolutely summing Hankel operators on Fock spaces and the Berger-Coburn phenomenon

TL;DR

This paper characterizes when Hankel operators on Fock spaces are r-summing, linking their norms to a specific function space, and explores the Berger-Coburn phenomenon in this context.

Contribution

It provides a precise characterization of r-summing Hankel operators on Fock spaces via the $ ext{IDA}^{ u,p}$-norm of symbols, extending understanding of their boundedness.

Findings

r-summing norm of $H_f$ is equivalent to the $ ext{IDA}^{ u,p}$-norm of $f$

Characterization of symbols for which Hankel operators are r-summing

Discussion of the Berger-Coburn phenomenon for these operators

Abstract

In this paper, for $1 \leq p, r < \infty$ we characterize those symbols $f$ so that the induced Hankel operators $H_f$ are $r$-summing from Fock spaces $F^p_\alpha$ to $L^p_\alpha$. The main result shows that the $r$-summing norm of $H_f$ is equivalent to the $\mathrm{IDA}^{\kappa, p}$-norm of $f$, where $\kappa$ is a positive number determined by $p$ and $r$, and the $\mathrm{IDA}$ space is as in [13]. As some application, we discuss the Berger-Coburn phenomenon for $r$-summing Hankel operators on Fock spaces.