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Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups

  • Cardona, Duván [1] ; Ruzhansky, Michael [2]
    1. [1] Ghent University

      Ghent University

      Arrondissement Gent, Bélgica

    2. [2] Queen Mary University of London

      Queen Mary University of London

      Reino Unido

  • Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 3, 2022, págs. 477-504
  • Idioma: inglés
  • DOI: 10.1007/s13348-021-00330-9
  • Enlaces
  • Resumen

    • We investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the Hörmander-Mihlin-Marcinkiewicz condition. In our analysis, we use the difference structure of the unitary dual of a compact Lie group. Our results cover the sharp Hörmander-Mihlin theorem on Lebesgue spaces and also other historical results on the subject.

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