Average radial integrability spaces of analytic functions

Abstract

In this paper we introduce the family of spaces RM(p, q), 1 ≤ p, q ≤ +∞. They are spaces of holomorphic functions in the unit disc with average radial integrability. This family contains the classical Hardy spaces (when p = ∞) and Bergman spaces (when p = q). We characterize the inclusion between RM(p1, q1) and RM(p2, q2) depending on the parameters. For 1 < p, q < ∞, our main result provides a characterization of the dual spaces of RM(p, q) by means of the boundedness of the Bergman projection. We show that RM(p, q) is separable if and only if q < +∞. In fact, we provide a method to build isomorphic copies of ∞ in RM(p, ∞).