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Asymptotic Behaviours in Fractional Orlicz–Sobolev Spaces on Carnot Groups

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Abstract

In this article, we define a class of fractional Orlicz–Sobolev spaces on Carnot groups, and in the spirit of the celebrated results of Bourgain–Brezis–Mironescu and of Maz’ya–Shaposhnikova, we study the asymptotic behaviour of the Orlicz functionals when the fractional parameter goes to 1 and 0.

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Acknowledgements

The authors would like to thank the anonymous referee for the suggestions that improved the paper.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123, Povo, Trento, Italy

    M. Capolli & A. Maione

  2. Departamento de Matemática, FCEyN - Universidad de Buenos Aires, Buenos Aires, Argentina

    A. M. Salort

  3. IMAS - CONICET Ciudad Universitaria, Pabellón I (1428) Av. Cantilo s/n., Buenos Aires, Argentina

    A. M. Salort

  4. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 20133, Milano, MI, Italy

    E. Vecchi

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  1. M. Capolli
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  2. A. Maione
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  3. A. M. Salort
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  4. E. Vecchi
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Correspondence to A. Maione.

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M.C. is supported by MIUR, Italy, GNAMPA of INDAM and University of Trento, Italy. A.M. is supported by MIUR, Italy, GNAMPA of INDAM and University of Trento, Italy.

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Capolli, M., Maione, A., Salort, A.M. et al. Asymptotic Behaviours in Fractional Orlicz–Sobolev Spaces on Carnot Groups. J Geom Anal 31, 3196–3229 (2021). https://doi.org/10.1007/s12220-020-00391-5

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  • DOI: https://doi.org/10.1007/s12220-020-00391-5

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