Mixing properties of a class of nonuniformly expanding maps — Application to Hölderian invariance principles

In this paper, we study the mixing properties of a class of nonuniformly expanding maps when the return time to the basis has a weak moment of order [Formula: see text], up to a slowly varying function. From these computations, we deduce an invariance principle in Hölder spaces for the partial sum process of Birkhoff sums of Hölder continuous observables. The results apply to a class of intermittent maps of the unit interval. For such a map, we also prove that the Hölder invariance principle remains true for BV observables.