  In this paper we introduce the family of spaces $RM(p,q)$, $1\leq p,q\leq
+\infty$. They are spaces of holomorphic functions in the unit disc with
average radial integrability. This family contains the classical Hardy spaces
(when $p=\infty$) 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 $1<p,q<\infty$, 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 $q<+\infty$. In fact, we
provide a method to build isomorphic copies of $\ell^\infty$ in $RM(p,\infty)$.
