A sharp trilinear inequality related to Fourier restriction on the circle
Emanuel CarneiroInstituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
Damiano FoschiUniversità di Ferrara, Italy
Diogo Oliveira e SilvaUniversität Bonn, Germany
Christoph ThieleUniversität Bonn, Germany
In this paper we prove a sharp trilinear inequality which is motivated by a program to obtain the sharp form of the 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.
Cite this article
Emanuel Carneiro, Damiano Foschi, Diogo Oliveira e Silva, Christoph Thiele, A sharp trilinear inequality related to Fourier restriction on the circle. Rev. Mat. Iberoam. 33 (2017), no. 4, pp. 1463–1486DOI 10.4171/RMI/978