Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality

Details Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality

2010-03-27

arxiv.org/abs/1003.5248v1

Mathematics

Functional Analysis

15 pages; contribution to the proceedings of the workshop at Florida Atlantic University, Boca Raton, Florida (October/Novembe

Scientific paper

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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