Sobolev spaces on graded lie groups

Veronique Fischer, Michael Ruzhansky

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31 Citations (SciVal)


In this article, we study the Lp-properties of powers of positive Rockland operators and define Sobolev spaces on general graded Lie groups. We establish that the defined Sobolev spaces are independent of the choice of a positive Rockland operator, and that they are interpolation spaces. Although this generalises the case of sub-Laplacians on stratified groups studied by G. Folland in [12], many arguments have to be different since Rockland operators are usually of higher degree than two. We also prove results regarding duality and Sobolev embeddings, together with inequalities of Hardy-Littlewood-Sobolev type and of Gagliardo-Nirenberg type.

Original languageEnglish
Pages (from-to)1671-1723
Number of pages53
JournalAnnales de l'institut Fourier
Issue number4
Publication statusPublished - 1 Jul 2017


  • Graded Lie groups
  • Harmonic analysis on nilpotent Lie groups
  • Heat semigroup
  • Rockland operators
  • Sobolev spaces

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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