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Published July 2016 | Submitted
Journal Article Open

Maximizers for the Stein–Tomas Inequality

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.

Additional Information

© 2016 Springer International Publishing. Received: March 21, 2016. Accepted: August 3, 2016. Published online October 4, 2016. R.L.F. and J.S. would like to thank D. Oliveira e Silva and C. Thiele for the summer school 'Sharp inequalities in harmonic analysis' in August 2015 which stimulated our interest in this project. Partial support by U.S. National Science Foundation DMS-1363432 (R.L.F.) and PHY-1265118 (E.H.L.) is acknowledged.

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Created:
August 20, 2023
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