Optimal Regularity Properties of the Riesz Potential Operator

Abstract

We prove continuity of the Riesz potential operator $R^s: E \mapsto {\mathcal C} H,$ in optimal couples $E, CH$, where $E$ is a rearrangement invariant function space and ${\mathcal C} H$ is the generalized Hölder-Zygmund space generated by a function space $H$.