Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality
Functional Analysis
2011-09-05 v2 Analysis of PDEs
Abstract
We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing functions due to Li and Zhu.
Cite
@article{arxiv.0904.4275,
title = {Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality},
author = {Rupert L. Frank and Elliott H. Lieb},
journal= {arXiv preprint arXiv:0904.4275},
year = {2011}
}
Comments
15 pages; references added and minor changes