Maximizers for the Stein-Tomas inequality
  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. 
Rupert L. Frank, Elliott H. Lieb, Julien Sabin
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