Big Hankel operators on Hardy spaces of strongly pseudoconvex domains

TL;DR

This paper studies big Hankel operators on Hardy spaces of strongly pseudoconvex domains in several complex variables and provides a new boundedness criterion for the one-variable case.

Contribution

It introduces a new necessary and sufficient condition for the boundedness of Hankel operators on Hardy spaces in the unit disc, extending previous results.

Findings

Characterization of bounded Hankel operators on Hardy spaces of strongly pseudoconvex domains

New boundedness criterion for the one-variable Hardy space case

Extension of results to several complex variables

Abstract

In this article, we investigate the (big) Hankel operators $H_f$ on Hardy spaces of strongly pseudoconvex domains with smooth boundaries in $\mathbb{C}^n$. We also give a necessary and sufficient condition for boundedness of the Hankel operator $H_f$ on the Hardy space of the unit disc, which is new in the setting of one variable.