Integral isoperimetric transference and dimensionless Sobolev inequalities

Abstract

We introduce the concept of Gaussian integral isoperimetric transference and show how it can be applied to obtain a new class of sharp Sobolev-Poincaré inequalities with constants independent of the dimension. In the special case of $L^q$ spaces on the unit $n-$dimensional cube our results extend the recent inequalities that were obtained in \cite{FKS} using extrapolation.

References in corpus (2)

• Pointwise Symmetrization Inequalities for Sobolev functions and applications
• Sobolev Inequalities: Symmetrization and Self Improvement via Truncation