Integration Operators in Average Radial Integrability Spaces of Analytic Functions

In this paper we introduce the family of spaces RM(p, q), 1 <= p, q <= infinity . They are spaces of holomorphic functions in the unit disc with average radial integrability. This family contains the classical Hardy spaces (when p = infinity) and Bergman spaces (when p = q). We characterize the inclusion between RM (p(1), q(1)) and RM(p(2), q(2)) depending on the parameters. For 1 < p, q < infinity, 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 < +infinity. In fact, we provide a method to build isomorphic copies of l(infinity) in RM(p, infinity). (C) 2021 The Author(s). Published by Elsevier Inc.