Remarks on a fractional diffusion transport equation with applications to the dissipative quasi-geostrophic equation

In this article I study H"older regularity for solutions of a transport equation based in the dissipative quasi-geostrophic equation. Following a recent idea of A. Kiselev and F. Nazarov, I will use the molecular characterization of local Hardy spaces in order to obtain information on H"older regularity of such solutions. This will be done by following the evolution of molecules in a backward equation.