Extremizers for the Airy-Strichartz inequality
Analysis of PDEs
2018-05-03 v2 Classical Analysis and ODEs
Abstract
We identify the compactness threshold for optimizing sequences of the Airy-- Strichartz inequality as an explicit multiple of the sharp constant in the Strichartz inequality. In particular, if the sharp constant in the Airy--Strichartz inequality is strictly smaller than this multiple of the sharp constant in the Strichartz inequality, then there is an optimizer for the former inequality. Our result is valid for the full range of Airy--Strichartz inequalities (except the endpoints) both in the diagonal and off-diagonal cases.
Cite
@article{arxiv.1712.04156,
title = {Extremizers for the Airy-Strichartz inequality},
author = {Rupert L. Frank and Julien Sabin and Rupert Frank},
journal= {arXiv preprint arXiv:1712.04156},
year = {2018}
}