On sharp Fourier extension from spheres in arbitrary dimensions

TL;DR

This paper establishes a new family of sharp Fourier extension inequalities from spheres in any dimension three and above, advancing understanding of harmonic analysis on spherical surfaces.

Contribution

It introduces a novel family of sharp $L^2$ to $L^4$ Fourier extension inequalities for spheres in all dimensions $d \,\geq\, 3$, generalizing previous results.

Findings

Proves sharp Fourier extension inequalities for spheres in arbitrary dimensions.

Identifies the optimal constants and extremizers for these inequalities.

Extends the theory of harmonic analysis on spherical surfaces.

Abstract

We prove a new family of sharp $L^2(\mathbb S^{d-1})\to L^4(\mathbb R^d)$ Fourier extension inequalities from the unit sphere $\mathbb S^{d-1}\subset \mathbb R^d$, valid in arbitrary dimensions $d\geq 3$.