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Function spaces via fractional Poisson kernel on Carnot groups and applications

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Abstract

We provide a new characterization of homogeneous Besov and Sobolev spaces in Carnot groups using the fractional heat kernel and Poisson kernel. We apply our results to study commutators involving fractional powers of the sub-Laplacian.

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Acknowledgements

The authors want to thank the referee for his/her careful reading of the paper and his/her insightful comments and suggestions that led to its improvement.

A. Pinamonti is a member of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

This work was supported by a grant from the Simons Foundation (#576219, G. Speight).

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Authors and Affiliations

  1. Department of Mathematics, Clark University, Worcester, MA, 01610, USA

    Ali Maalaoui

  2. Department of Mathematics, University of Trento, Via Sommarive 14, 38123, Povo (Trento), Italy

    Andrea Pinamonti

  3. Department of Mathematical Sciences, University of Cincinnati, 2815 Commons Way, Cincinnati, OH, 45221, USA

    Gareth Speight

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  1. Ali Maalaoui
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Correspondence to Ali Maalaoui.

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Maalaoui, A., Pinamonti, A. & Speight, G. Function spaces via fractional Poisson kernel on Carnot groups and applications. JAMA 149, 485–527 (2023). https://doi.org/10.1007/s11854-022-0255-y

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  • DOI: https://doi.org/10.1007/s11854-022-0255-y

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