Real Interpolation method, Lorentz spaces and refined Sobolev inequalities

Diego Chamorro (1) , Pierre-Gilles Lemarié-Rieusset (1)

1 LAP - Laboratoire Analyse et Probabilités

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.

Mots clés: Lorentz spaces; refined Sobolev inequalities: real interpolation spaces; Besov spaces

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Diego Chamorro, Pierre-Gilles Lemarié-Rieusset. Real Interpolation method, Lorentz spaces and refined Sobolev inequalities. 2012. ⟨hal-00751688⟩