Mathematical Research Letters

Volume 25 (2018)

Number 3

Nonexistence of extremizers for certain convex curves

Pages: 973 – 987

DOI: http://dx.doi.org/10.4310/MRL.2018.v25.n3.a12

Author

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

Abstract

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.

Keywords

extremizers, Tomas–Stein inequality, convolution of arclength measure

2010 Mathematics Subject Classification

42A05

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Received 13 December 2012