Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality
Functional Analysis
2010-03-30 v1 Analysis of PDEs
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 .
Keywords
Cite
@article{arxiv.1003.5248,
title = {Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality},
author = {Rupert L. Frank and Elliott H. Lieb},
journal= {arXiv preprint arXiv:1003.5248},
year = {2010}
}
Comments
15 pages; contribution to the proceedings of the workshop at Florida Atlantic University, Boca Raton, Florida (October/November 2009)