Atomic decomposition and weak factorization for Bergman–Orlicz spaces
Volume 160 / 2020
Colloquium Mathematicum 160 (2020), 223-245
MSC: Primary 47B35; Secondary 32A35, 32A37.
DOI: 10.4064/cm7597-3-2019
Published online: 31 January 2020
Abstract
For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman–Orlicz spaces of holomorphic functions in $L^\Phi _\alpha (\mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for functions in the Bergman–Orlicz space $\mathcal A^\Phi _\alpha (\mathbb B^n)$ where $\Phi $ is either a convex or a concave growth function. We then prove weak factorization theorems involving the Bloch space and a Bergman–Orlicz space, and also weak factorization theorems involving two Bergman–Orlicz spaces.
