Factoring Sobolev inequalities through classes of functions

Abstract

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.

References in corpus (3)

• Pointwise Symmetrization Inequalities for Sobolev functions and applications
• Sobolev Inequalities: Symmetrization and Self Improvement via Truncation
• An Asymmetric Affine Pólya--Szegö Principle