An Asymmetric Affine Pólya--Szegö Principle

Details An Asymmetric Affine Pólya--Szegö Principle An Asymmetric Affine Pólya--Szegö Principle

2009-08-11

arxiv.org/abs/0908.1557v4

Mathematics

Functional Analysis

20 pages

Scientific paper

An affine rearrangement inequality is established which strengthens and
implies the recently obtained affine P\'olya--Szeg\"o symmetrization principle
for functions on $\mathbb{R}^n$. 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.

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