Real Interpolation method, Lorentz spaces and refined Sobolev   inequalities
  In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen. Our approach is based in the characterization of Lorentz spaces as real interpolation spaces. We will also study the sharpness and optimality of these inequalities. 
Diego Chamorro, Pierre-Gilles Lemari\'e-Rieusset
math.AP math.FA