Sharpness of the Mockenhaupt-Mitsis-Bak-Seeger Restriction Theorem in Higher Dimensions

TL;DR

This paper demonstrates that the range of exponents in a key Fourier restriction theorem is optimal for many measures in higher dimensions, extending previous sharpness results.

Contribution

It establishes the sharpness of the Fourier restriction theorem's exponent range in higher dimensions for a broad class of measures, generalizing prior work.

Findings

Range of exponents is sharp for many measures in higher dimensions

Extends sharpness results of Hambrook and Łaba to higher dimensions

Confirms optimality of Fourier restriction estimates in a broad setting

Abstract

We prove the range of exponents in the general $L^2$ Fourier restriction theorem due to Mockenhaupt, Mitsis, Bak and Seeger is sharp for a large class of measures on $\mathbb{R}^d$. This extends to higher dimensions the sharpness result of Hambrook and {\L}aba.