Factorization and Atomic Decomposition in Hardy-Orlicz Spaces on the Upper Half-Plane with Applications to Hankel Operators

Abstract

In this work, we establish a strong factorization for Hardy-Orlicz spaces on the upper half-plane. We show that the product of two functions belonging respectively to Hardy-Orlicz spaces $H^{Φ_{1}}$ and $H^{Φ_{2}}$ lies in a third space $H^{Φ_{3}}$, and every holomorphic function in $H^{Φ_{3}}$ admits such a decomposition. We then provide an atomic decomposition for certain Hardy-Orlicz spaces, which allows us to describe the topological dual of these spaces when the associated function is concave. Finally, these results are applied to the study of the continuity of the Hankel operators in this setting.