The Extremizer Problem for the Tomas-Stein Inequality for the Two Dimensional Sphere
Abstract
The Tomas-Stein inequality for the sphere is a fundamental inequality in harmonic analysis. Motivated by the recent progress of the concentration-compactness (CC) approach in solving the global wellposedness and scattering problems of nonlinear dispersive equations such as Schr\”odinger and wave equations, we investigate the maximizers problems for this inequality. The approach happens to be the profile decomposition that is of similar flavor as the CC approach. This is a joint wok with M. Christ.
