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.
|Journal||Mathematical Research Letters|
|Publication status||Published - 1 Mar 2018|
Bibliographical note11 pages
- Tomas-Stein inequality
- convolution of arclength measure