  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 Holder 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.
