Maximizers for the Stein–Tomas Inequality |
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| Authors: | Rupert L Frank Elliott H Lieb Julien Sabin |
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| Institution: | 1.Departments of Mathematics 253-37,Caltech,Pasadena,USA;2.Departments of Mathematics and Physics,Princeton University,Princeton,USA;3.Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay,Orsay,France |
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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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