Existence of Extremals for a Fourier Restriction Inequality

Abstract

The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping $f\mapsto \widehat{f\sigma }$ is bounded from $<(S^2)$ to $L^4({\mathbb{R}}^3)$. We prove that there exist functions which extremize this inequality, and that any extremizing sequence of nonnegative functions has a subsequence which converges to an extremizer.

arXiv comment52 pages

References in corpus (2)

• Quasiextremals for a Radon-like transform
• Heat-flow monotonicity of Strichartz norms

Cited by in corpus (7)

• Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid
• Analyticity of extremisers to the Airy Strichartz inequality
• On extremals for a Radon-like transform
• Optimal constants and extremisers for some smoothing estimates
• On extremizers for Strichartz estimates for higher order Schrödinger equations
• Nonexistence of extremizers for certain convex curves
• Extremizers for Fourier restriction inequalities: convex arcs