Extremizers for Fourier restriction inequalities: convex arcs
  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. 
Diogo Oliveira e Silva
math.CA math.AP