A sharp trilinear inequality related to Fourier restriction on the circle

Emanuel Carneiro, Diogo Oliveira e Silva, Damiano Foschi, Christoph Thiele

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

Bibliographical note

19 pages, 2 tables


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


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