Hankel operators on holomorphic Hardy-Orlicz spaces

TL;DR

This paper characterizes bounded Hankel operators between Hardy-Orlicz spaces on the unit ball, extending previous work to new growth function cases and establishing weak factorization theorems for these spaces.

Contribution

It provides a comprehensive characterization of Hankel symbols for boundedness between Hardy-Orlicz spaces with concave or convex growth functions and introduces weak factorization results.

Findings

Characterization of symbols for bounded Hankel operators on Hardy-Orlicz spaces.

Extension of previous results to new growth function cases.

Weak factorization theorems for Hardy-Orlicz functions with concave growth.

Abstract

We characterize the symbols of Hankel operators that ex- tend into bounded operators from the Hardy-Orlicz $H^{\Phi_1} (\mathbb B^n)$ into $H^{\Phi_2} (\mathbb B^n)$ in the unit ball of Cn, in the case where the growth functions $?\Phi_1$ and $\Phi_2$ are either concave or convex. The case where the growth functions are both concave has been studied by Bonami and Sehba. We also obtain several weak factorization theorems for functions in $H^\Phi(\mathbb B^n)$, with concave growth function, in terms of products of Hardy-Orlicz functions with convex growth functions.