A sharp trilinear inequality related to Fourier restriction on the circle

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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.

Bibliographic note

19 pages, 2 tables


Original languageEnglish
Pages (from-to)1463–1486
Number of pages24
JournalRevista Matematica Iberoamericana
Issue number4
Publication statusPublished - 2017


  • math.CA, 42B10, Circle, Fourier restriction, Sharp inequalities, Extremizers, Convolution of surface measures, Bessel functions