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

TL;DR

This paper establishes the optimal exponent in the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem across all dimensions and parameter ranges, using a deterministic construction that also produces Salem sets.

Contribution

It proves the optimality of the Fourier restriction exponent in all dimensions and parameters, providing a deterministic construction that yields Salem sets.

Findings

Optimality of the Fourier restriction exponent in all dimensions

Deterministic construction of Salem sets

Extension of the theorem to full parameter range

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.