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arXiv · 0908.1557

An Asymmetric Affine Pólya--Szegö Principle

Christoph Haberl·Franz E. Schuster·Jie Xiao
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Abstract

An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Pólya--Szegö 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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Christoph Haberl, Franz E. Schuster, Jie Xiao. 2009-08-15. An Asymmetric Affine Pólya--Szegö Principle. https://arxiv.org/abs/0908.1557

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