  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 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.
