Revista Matemática Iberoamericana


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Volume 33, Issue 4, 2017, pp. 1463–1486
DOI: 10.4171/RMI/978

Published online: 2017-11-17

A sharp trilinear inequality related to Fourier restriction on the circle

Emanuel Carneiro[1], Damiano Foschi[2], Diogo Oliveira e Silva[3] and Christoph Thiele[4]

(1) Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
(2) Università di Ferrara, Italy
(3) Universität Bonn, Germany
(4) Universität Bonn, Germany

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.

Keywords: Circle, Fourier restriction, sharp inequalities, extremizers, convolution of surface measures, Bessel functions

Carneiro Emanuel, Foschi Damiano, Oliveira e Silva Diogo, Thiele Christoph: A sharp trilinear inequality related to Fourier restriction on the circle. Rev. Mat. Iberoamericana 33 (2017), 1463-1486. doi: 10.4171/RMI/978