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Besov and Triebel–Lizorkin spaces on Lie groups

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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.

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Acknowledgements

The authors wish to thank Andrea Carbonaro for useful conversations.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange”, Dipartimento di Eccellenza 2018–2022, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy

    Tommaso Bruno & Maria Vallarino

  2. Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133, Milan, Italy

    Marco M. Peloso

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  1. Tommaso Bruno
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  2. Marco M. Peloso
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  3. Maria Vallarino
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Correspondence to Marco M. Peloso.

Additional information

Communicated by Loukas Grafakos.

In memory of Elias M. Stein.

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All authors are partially supported by the grant PRIN 2015 Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis, and are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Bruno, T., Peloso, M.M. & Vallarino, M. Besov and Triebel–Lizorkin spaces on Lie groups. Math. Ann. 377, 335–377 (2020). https://doi.org/10.1007/s00208-019-01927-z

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  • DOI: https://doi.org/10.1007/s00208-019-01927-z

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