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Riesz and Poisson-Jensen Representation Formulas for a Class of Ultraparabolic Operators on Lie Groups

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Abstract

The aim of this paper is to give some representation formulas of Riesz and Poisson-Jensen type for super-solutions to a class of hypoelliptic ultraparabolic operators \(\mathcal{L}\) on a homogeneous Lie group \(\mathbb{L}\). Our results complete the ones obtained in Cinti (Math Scand 100:1–21, 2007). We also provide a suitable theory for \(\mathcal{L}\)-Green functions and for \(\mathcal{L}\)-Green potentials of Radon measures. The proofs mostly rely on the use of appropriate techniques relevant to the Potential Theory for \(\mathcal{L}\).

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126, Bologna, Italy

    Chiara Cinti & Ermanno Lanconelli

Authors
  1. Chiara Cinti
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  2. Ermanno Lanconelli
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Correspondence to Chiara Cinti.

Additional information

Investigation supported by University of Bologna. Funds for selected research topics.

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Cinti, C., Lanconelli, E. Riesz and Poisson-Jensen Representation Formulas for a Class of Ultraparabolic Operators on Lie Groups. Potential Anal 30, 179–200 (2009). https://doi.org/10.1007/s11118-008-9112-6

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  • DOI: https://doi.org/10.1007/s11118-008-9112-6

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