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

Abstract

In this paper, for $1\le p,r<\infty$ we characterize those symbols $f$ so that the induced Hankel operators $H_f$ are $r$-summing from Fock spaces $F_{\alpha }^p$ to $L_{\alpha }^p$. 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.