The Stein-Tomas inequality under the effect of symmetries

Abstract

We prove new Fourier restriction estimates to the unit sphere $S^{d-1}$ on the class of $O(d-k)\times O(k)$-symmetric functions, for every $d\ge 4$ and $2\le k\le d-2$. As an application, we establish the existence of maximizers for the endpoint Stein--Tomas inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp.

arXiv comment32 pages, 1 figure