Atomic decomposition and Weak Factorization for Bergman-Orlicz spaces

Abstract

For ${\mathbb{B}}^n$ the unit ball of ${\mathbb{C}}^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L_{\alpha }^{\Phi }({\mathbb{B}}^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for functions in the Bergman-Orlicz space ${\mathcal{A}}_{\alpha }^{\Phi }({\mathbb{B}}^n)$ where $\Phi$ is either convex or 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.