Factoring Sobolev inequalities through classes of functions
  We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp) connection between them. 
David Alonso-Guti\'errez, Jes\'us Bastero and Julio Bernu\'es
math.FA