Besov and Triebel–Lizorkin spaces on Lie groups

  • Tommaso Bruno
  • Marco M. PelosoEmail author
  • Maria Vallarino


In this paper we develop a theory of Besov and Triebel–Lizorkin spaces on general noncompact connected Lie groups endowed with a sub-Riemannian structure. Such spaces are defined by means of hypoelliptic sub-Laplacians with drift, and endowed with a measure whose density with respect to a right Haar measure is a continuous positive character of the group. We prove several equivalent characterizations of their norms, we establish comparison results also involving Sobolev spaces of recent introduction, and investigate their complex interpolation and algebra properties.

Mathematics Subject Classification

46E35 22E30 43A15 



The authors wish to thank Andrea Carbonaro for useful conversations.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange”Dipartimento di Eccellenza 2018–2022, Politecnico di TorinoTurinItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanItaly

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