Extremizers for Fourier restriction inequalities: convex arcs

Abstract

We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with colinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing sequence of nonnegative functions has a subsequence which converges to an extremizer.

46 pages. arXiv admin note: text overlap with arXiv:1006.4319 by other authors

References in corpus (3)

• Existence of Extremals for a Fourier Restriction Inequality
• On extremals for a Radon-like transform
• On the extremizers of an adjoint Fourier restriction inequality