Exponential decay of correlations for unbounded observables

We consider nonuniformly hyperbolic dynamical systems with exponential decay of correlations, and show that exponential decay holds for pairs of observables v in L^p, w in L^q for which the corresponding local Holder constants also lie in L^p and L^q, with 1/p+1/q<1. Along the way, we give a particularly simple proof of quasicompactness for the one-sided transfer operator.