Sharpness of the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem in all dimensions

Abstract

We prove the optimality of the exponent in the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem in all dimensions $d$ and the full parameter range $0<a,b<d$. Our construction is deterministic and also yields Salem sets.