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.
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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