Mathematical Research Letters
Volume 25 (2018)
Nonexistence of extremizers for certain convex curves
Pages: 973 – 987
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