Integral isoperimetric transference and dimensionless Sobolev inequalities
Functional Analysis
2017-05-30 v1
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-Poincar\'{e} inequalities with constants independent of the dimension. In the special case of spaces on the unit dimensional cube our results extend the recent inequalities that were obtained in \cite{FKS} using extrapolation.
Cite
@article{arxiv.1309.1980,
title = {Integral isoperimetric transference and dimensionless Sobolev inequalities},
author = {Joaquim Martin and Mario Milman},
journal= {arXiv preprint arXiv:1309.1980},
year = {2017}
}