Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality
Functional Analysis
2011-10-26 v1
Abstract
We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincar'e inequality for the Gaussian measure.
Keywords
Cite
@article{arxiv.1110.5551,
title = {Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality},
author = {S. Artstein-Avidan and B. Klartag and C. Schuett and E. Werner},
journal= {arXiv preprint arXiv:1110.5551},
year = {2011}
}