Spectral projectors, resolvent, and Fourier restriction on the hyperbolic space

Pierre Germain, Tristan Léger

Research output: Contribution to journalArticlepeer-review


We develop a unified approach to proving Lp−Lq boundedness of spectral projectors, the resolvent of the Laplace-Beltrami operator and its derivative on Hd. In the case of spectral projectors, and when p and q are in duality, the dependence of the implicit constant on p is shown to be sharp. We also give partial results on the question of Lp−Lq boundedness of the Fourier extension operator. As an application, we prove smoothing estimates for the free Schrödinger equation on Hd and a limiting absorption principle for the electromagnetic Schrödinger equation with small potentials.

Original languageEnglish (US)
Article number109918
JournalJournal of Functional Analysis
Issue number2
StatePublished - Jul 15 2023


  • Fourier restriction
  • Hyperbolic space
  • Resolvent
  • Smoothing estimates

ASJC Scopus subject areas

  • Analysis


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