Conditional existence of maximizers for the Tomas-Stein inequality for the sphere

Shuanglin Shao, Ming Wang

The Tomas-Stein inequality for a compact subset $\Gamma$ of the sphere $S^d$ states that the mapping $f\mapsto \widehat{f\sigma }$ is bounded from $L^2(\Gamma ,\sigma )$ to $L^{2+4/d}({\mathbb{R}}^{d+1})$. Then co…