Hankel operators and weak factorization for Hardy–Orlicz spaces

Aline Bonami¹ ; Sandrine Grellier¹

¹Fédération Denis Poisson (MAPMO-UMR 6628) Département de Mathématiques Université d'Orléans 45067 Orléans Cedex 2, France

Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 107-132

Résumé

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 $\mathcal H^1(\Omega)$.

Détail

DOI : 10.4064/cm118-1-5

Keywords: study holomorphic hardy orlicz spaces cal phi omega where omega unit ball generally convex domain finite type strictly pseudoconvex domain mathbb function phi particular cal omega subset cal phi omega subset cal omega develop maximal characterizations atomic molecular decompositions prove weak factorization theorems involving space bmoa omega consequence characterize those hankel operators which bounded mathcal phi omega mathcal omega