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

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 Łaba.

References in corpus (3)

• On the sharpness of Mockenhaupt's restriction theorem
• Convolution Powers of Salem Measures with Applications
• Sets of Salem type and sharpness of the $L^2$-Fourier restriction theorem

Cited by in corpus (2)

• Near-optimal restriction estimates for Cantor sets on the parabola
• Existence of traveling waves for a fourth order Schr\" odinger equation with mixed dispersion in the Helmholtz regime