Maximizers for the Stein-Tomas inequality
Classical Analysis and ODEs
2016-03-25 v1 Analysis of PDEs
Functional Analysis
Abstract
We give a necessary and sufficient condition for the precompactness of all optimizing sequences for the Stein-Tomas inequality. In particular, if a well-known conjecture about the optimal constant in the Strichartz inequality is true, we obtain the existence of an optimizer in the Stein-Tomas inequality. Our result is valid in any dimension.
Cite
@article{arxiv.1603.07658,
title = {Maximizers for the Stein-Tomas inequality},
author = {Rupert L. Frank and Elliott H. Lieb and Julien Sabin},
journal= {arXiv preprint arXiv:1603.07658},
year = {2016}
}
Comments
37 pages