Extremizers for adjoint Fourier restriction on hyperboloids: the higher dimensional case

Abstract

We prove that in dimensions $d\ge 3$, the non-endpoint, Lorentz-invariant $L^2\to L^p$ adjoint Fourier restriction inequality on the $d$-dimensional hyperboloid ${\mathbb{H}}^d\subseteq {\mathbb{R}}^{d+1}$ possesses maximizers. The analogous result had been previously established in dimensions $d=1,2$ using the convolution structure of the inequality at the lower endpoint (an even integer); we obtain the generalization by using tools from bilinear restriction theory.

20 pages