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Subharmonic functions on Carnot groups

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Abstract.

 Many results of classical Potential Theory are extended to sub-Laplacians ▵𝔾 on Carnot groups 𝔾. Some characterizations of ▵𝔾-subharmonicity, representation formulas of Poisson-Jensen's kind and Nevanlinna-type theorems are proved. We also characterize the Riesz-measure related to bounded-above ▵𝔾-subharmonic functions in ℝN.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy (e-mail: bonfigli@dm.unibo.it; lanconel@dm.unibo.it), , , , , , IT

    Andrea Bonfiglioli & Ermanno Lanconelli

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  1. Andrea Bonfiglioli
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  2. Ermanno Lanconelli
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Received: 21 June 2000 / Revised version: 12 March 2002 / Published online: 2 December 2002

RID="★"

ID="★" Investigation supported by University of Bologna. Funds for selected research topics.

Mathematics Subject Classification (2000): 31B05, 35J70, 35H20

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Bonfiglioli, A., Lanconelli, E. Subharmonic functions on Carnot groups. Math. Ann. 325, 97–122 (2003). https://doi.org/10.1007/s00208-002-0371-z

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  • DOI: https://doi.org/10.1007/s00208-002-0371-z

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