Hankel operators and weak factorization for Hardy–Orlicz spaces
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 107-132
MSC: 32A35, 32A37, 47B35.
DOI: 10.4064/cm118-1-5
Abstract
We study the holomorphic Hardy–Orlicz spaces ${\cal H}^{\Phi}(\Omega)$, where $\Omega$ is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in ${\mathbb C}^n$. The function $\Phi$ is in particular such that ${\cal H}^{1}(\Omega)\subset {\cal H}^{\Phi}(\Omega)\subset {\cal H}^{p}(\Omega)$ for some $p>0$. We develop maximal characterizations, atomic and molecular decompositions. We then prove weak factorization theorems involving the space ${\it BMOA}(\Omega)$. As a consequence, we characterize those Hankel operators which are bounded from $\mathcal H^\Phi(\Omega)$ into $\mathcal H^1(\Omega)$.
