A sharp trilinear inequality related to Fourier restriction on the circle

Abstract

In this paper we prove a sharp trilinear inequality which is motivated by a program to obtain the sharp form of the $L^2-L^6$ Tomas-Stein adjoint restriction inequality on the circle. Our method uses intricate estimates for integrals of sixfold products of Bessel functions developed in a companion paper. We also establish that constants are local extremizers of the Tomas-Stein adjoint restriction inequality as well as of another inequality appearing in the program.

19 pages, 2 tables

References in corpus (2)

• A sharp bilinear estimate for the Klein-Gordon equation in arbitrary space-time dimensions
• On Restricting Cauchy-Pexider Equations to Submanifolds

Cited by in corpus (10)

• Extremizers for Fourier restriction on hyperboloids
• Sharp mixed norm spherical restriction
• Sharp Strichartz inequalities for fractional and higher order Schrödinger equations
• Local maximizers of adjoint Fourier restriction estimates for the cone, paraboloid and sphere
• Band-limited maximizers for a Fourier extension inequality on the circle
• A comparison principle for convolution measures with applications
• Some recent progress on sharp Fourier restriction theory
• Delocalisation of one-dimensional marginals of product measures and the capacity of LTI discrete channels
• On profile decomposition for Airy type equation
• On smoothness of extremizers of the Tomas-Stein inequality for $S^1$