Weak Factorization and Hankel Forms for Bergman–Orlicz Spaces on the Unit Ball

Abstract

Let $${\mathbb {B}}^n$$ be the unit ball of $${\mathbb {C}}^n$$ and $${\mathcal {A}}^\Phi _\alpha ({\mathbb {B}}^n)$$ be the Bergman–Orlicz space, consisting of holomorphic functions in $$L^\Phi _\alpha ({\mathbb {B}}^n)$$ . We characterize bounded Hankel operators between some Bergman–Orlicz spaces $${\mathcal {A}}^{\Phi _1}_\alpha ({\mathbb {B}}^n)$$ and $$\mathcal A^{\Phi _2}_\alpha ({\mathbb {B}}^n)$$ where $$\Phi _1$$ and $$\Phi _2$$ are convex growth functions. We then obtain weak factorization theorems for $${\mathcal {A}}^\Phi _\alpha ({\mathbb {B}}^n)$$ , with $$\Phi $$ a convex growth function, into two Bergman–Orlicz spaces, generalizing the main result obtained in Pau and Zhao (Math Ann 363:363–383, 2015).