Extremizers for Fourier restriction on hyperboloids

  • Mateus Sousa

    IMPA – Instituto de Matemática Pura e Aplicada, Rio de Janeiro – RJ, 22460-320, Brazil
  • Emanuel Carneiro

    IMPA – Instituto de Matemática Pura e Aplicada, Rio de Janeiro – RJ, 22460-320, Brazil
  • Diogo Oliveira e Silva

    Hausdorff Center for Mathematics, 53115 Bonn, Germany
Extremizers for Fourier restriction on hyperboloids cover
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Abstract

The adjoint Fourier restriction inequality on the d-dimensional hyperboloid holds provided , if , and , if . Quilodrán [35] recently found the values of the optimal constants in the endpoint cases and showed that the inequality does not have extremizers in these cases. In this paper we answer two questions posed in [35], namely: (i) we find the explicit value of the optimal constant in the endpoint case (the remaining endpoint for which p is an even integer) and show that there are no extremizers in this case; and (ii) we establish the existence of extremizers in all non-endpoint cases in dimensions . This completes the qualitative description of this problem in low dimensions.

Cite this article

Mateus Sousa, Emanuel Carneiro, Diogo Oliveira e Silva, Extremizers for Fourier restriction on hyperboloids. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, pp. 389–415

DOI 10.1016/J.ANIHPC.2018.06.001