An Asymmetric Affine P\'olya--Szeg\"o Principle
Functional Analysis
2009-08-15 v4 Differential Geometry
Abstract
An affine rearrangement inequality is established which strengthens and implies the recently obtained affine P\'olya--Szeg\"o symmetrization principle for functions on . Several applications of this new inequality are derived. In particular, a sharp affine logarithmic Sobolev inequality is established which is stronger than its classical Euclidean counterpart.
Keywords
Cite
@article{arxiv.0908.1557,
title = {An Asymmetric Affine P\'olya--Szeg\"o Principle},
author = {Christoph Haberl and Franz E. Schuster and Jie Xiao},
journal= {arXiv preprint arXiv:0908.1557},
year = {2009}
}
Comments
20 pages