Mathematical Research Letters

Volume 25 (2018)

Number 3

Nonexistence of extremizers for certain convex curves

Pages: 973 – 987



Diogo Oliveira e Silva (Hausdorff Center for Mathematics, Universität Bonn, Germany)


We establish the nonexistence of extremizers for a local Fourier restriction inequality on a certain class of planar convex curves whose curvature satisfies a natural assumption.We accomplish this by studying the local behavior of the triple convolution of the arclength measure on the curve with itself, and show in particular that every extremizing sequence concentrates at a point on the curve.


extremizers, Tomas–Stein inequality, convolution of arclength measure

2010 Mathematics Subject Classification


Received 13 December 2012

Published 3 August 2018