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.