A sharp trilinear inequality related to Fourier restriction on the circle

• Emanuel Carneiro ^[1] ; Damiano Foschi ^[2] ; Diogo Oliveira e Silva ^[3] ; Christoph Thiele ^[3]
  1. [1] Instituto de Matemática Pura e Aplicada
  2. [2] Università di Ferrara
  3. [3] Universität Bonn

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 4, 2017, págs. 1463-1486
• Idioma: inglés
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• Resumen

  • In this paper we prove a sharp trilinear inequality which is motivated by a program to obtain the sharp form of the L2−L6 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.