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Extremizers for the Airy–Strichartz inequality

Frank, Rupert L. and Sabin, Julien (2018) Extremizers for the Airy–Strichartz inequality. Mathematische Annalen, 372 (3-4). pp. 1121-1166. ISSN 0025-5831. http://resolver.caltech.edu/CaltechAUTHORS:20180604-091720191

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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.


Item Type:Article
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https://doi.org/10.1007/s00208-018-1695-7DOIArticle
https://rdcu.be/SQmhPublisherFree ReadCube access
https://arxiv.org/abs/1712.04156arXivDiscussion Paper
Additional Information:© 2018 Springer-Verlag GmbH Germany, part of Springer Nature. Received: 11 December 2017; Revised: 30 April 2018; First Online: 02 June 2018. The authors would like to thank Terence Tao for suggesting to look at this problem for general p and Diogo Oliveira e Silva, Réne Quilodrán and an anonymous referee for discussions concerning the Ap,R problem. Partial support through US National Science Foundation Grant DMS-1363432 (R.L.F.) is also acknowledged.
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Funding AgencyGrant Number
NSFDMS-1363432
Record Number:CaltechAUTHORS:20180604-091720191
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180604-091720191
Official Citation:Frank, R.L. & Sabin, J. Math. Ann. (2018) 372: 1121. https://doi.org/10.1007/s00208-018-1695-7
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86775
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 Jun 2018 18:03
Last Modified:29 Nov 2018 19:23

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