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Maximizers for the Stein–Tomas Inequality

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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.

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Authors and Affiliations

  1. Departments of Mathematics 253-37, Caltech, Pasadena, CA, 91125, USA

    Rupert L. Frank

  2. Departments of Mathematics and Physics, Princeton University, Princeton, NJ, 08544, USA

    Elliott H. Lieb

  3. Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405, Orsay, France

    Julien Sabin

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  1. Rupert L. Frank
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  2. Elliott H. Lieb
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  3. Julien Sabin
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Correspondence to Rupert L. Frank.

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Frank, R.L., Lieb, E.H. & Sabin, J. Maximizers for the Stein–Tomas Inequality. Geom. Funct. Anal. 26, 1095–1134 (2016). https://doi.org/10.1007/s00039-016-0380-9

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  • DOI: https://doi.org/10.1007/s00039-016-0380-9

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