Decay of correlations for non-Hölder observables

We consider the general question of estimating decay of correlations for non-uniformly expanding maps, for classes of observables which are much larger than the usual class of Hölder continuous functions. Our results give new estimates for many non-uniformly expanding systems, including Manneville-Pomeau maps, many one-dimensional systems with critical points, and Viana maps. In many situations, we also obtain a Central Limit Theorem for a much larger class of observables than usual. Our main tool is an extension of the coupling method introduced by L.-S. Young for estimating rates of mixing on certain non-uniformly expanding tower maps.