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

摘要

Let Bn be the unit ball of Cn and A phi(Bn) be the Bergman-Orlicz space, consisting of holomorphic functions in L phi(Bn). We characterize bounded Hankel operators between some Bergman-Orlicz spaces A phi 1(Bn) and A phi 2(Bn) where phi 1 and phi 2 are convex growth functions. We then obtain weak factorization theorems for A phi(Bn), 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).