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arXiv · 1003.5248

Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality

Rupert L. Frank·Elliott H. Lieb
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Abstract

We introduce the concept of spherical (as distinguished from planar) reflection positivity and use it to obtain a new proof of the sharp constants in certain cases of the HLS and the logarithmic HLS inequality. Our proofs relies on an extension of a work by Li and Zhu which characterizes the minimizing functions of the type $(1+|x|^2)^{-p}$.

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Rupert L. Frank, Elliott H. Lieb. 2010-03-27. Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. https://arxiv.org/abs/1003.5248

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