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arXiv · 1805.03754

Atomic decomposition and Weak Factorization for Bergman-Orlicz spaces

David Bekolle·Aline Bonami·Edgar Tchoundja
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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 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.

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David Bekolle, Aline Bonami, Edgar Tchoundja. 2018-05-09. Atomic decomposition and Weak Factorization for Bergman-Orlicz spaces. https://arxiv.org/abs/1805.03754

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