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Fourier multipliers on graded Lie groups

Volume 165 / 2021

Véronique Fischer, Michael Ruzhansky Colloquium Mathematicum 165 (2021), 1-30 MSC: Primary 43A80; Secondary 43A22, 22E25. DOI: 10.4064/cm7817-6-2020 Published online: 29 October 2020


We study multipliers on graded nilpotent Lie groups defined via group Fourier transform. More precisely, we show that Hörmander-type conditions on the Fourier multipliers imply $L^p$-boundedness. We express these conditions using difference operators and positive Rockland operators. We also obtain a more refined condition using Sobolev spaces on the dual of the group which are defined and studied in this paper.


  • Véronique FischerDepartment of Mathematical Sciences
    University of Bath
    Claverton Down
    Bath BA2 7AY, United Kingdom
  • Michael RuzhanskyDepartment of Mathematics:
    Analysis, Logic and Discrete Mathematics
    Ghent University
    Krijgslaan 281, Building S8
    B-9000 Gent, Belgium
    School of Mathematical Sciences
    Queen Mary University of London
    Mile End Road
    London E1 4NS, United Kingdom

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