  We are interested in some properties related to the solutions of non-local
diffusion equations with divergence free drift. Existence, maximum principle
and a positivity principle are proved. In order to study Holder regularity, we
apply a method that relies in the Holder-Hardy spaces duality and in the
molecular characterisation of local Hardy spaces. In these equations, the
diffusion is given by L\'evy-type operators with an associated L\'evy measure
satisfying some upper and lower bounds.
