Math. Ann. Mathematische Annalen https://doi.org/10.1007/s00208-018-1695-7 1,2 3 Rupert L. Frank · Julien Sabin Received: 11 December 2017 / Revised: 30 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 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. 1 Introduction The solution of the Cauchy problem for the Airy equation ∂ v + ∂ v = 0, t ∈ R, x ∈ R, (1.1) v = u ∈ L (R) |t =0 Communicated by Loukas Grafakos. Rupert L. Frank email@example.com Julien Sabin Julien.Sabin@math.u-psud.fr Mathematisches Institut, Ludwig-Maximilans Universität München, Theresienstr. 39, 80333 Munich, Germany Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France 123 R. L. Frank, J. Sabin −t ∂ may be
Mathematische Annalen – Springer Journals
Published: Jun 2, 2018
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