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.
|Original language||English (US)|
|Number of pages||40|
|Journal||Geometric and Functional Analysis|
|State||Published - Jul 1 2016|
All Science Journal Classification (ASJC) codes
- Geometry and Topology