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
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• 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.