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A Poisson–Jensen Type Representation Formula for Subharmonic Functions on Stratified Lie Groups

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Abstract

The aim of this paper is to prove a representation formula of Poisson–Jensen type on bounded domains Ω for subharmonic functions related to sub-Laplacians ΔG on stratified Lie groups G. Our result gives a complete answer to a question arisen in Math. Ann. 325 (2003), 97–122, where the additional hypothesis that Ω is regular for the Dirichlet problem related to ΔG was made: here we treat the case of arbitrary bounded domains Ω, omitting the hypothesis of regularity. In order to prove our representation formula, an ad-hoc theory of polar sets and capacity with respect to ΔG is also provided.

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Authors and Affiliations

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

    Andrea Bonfiglioli & Chiara Cinti

Authors
  1. Andrea Bonfiglioli
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  2. Chiara Cinti
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Corresponding author

Correspondence to Andrea Bonfiglioli.

Additional information

Mathematics Subject Classifications (2000)

Primary 31B10, 31B15; Secondary 35J70, 43A80.

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

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Bonfiglioli, A., Cinti, C. A Poisson–Jensen Type Representation Formula for Subharmonic Functions on Stratified Lie Groups. Potential Anal 22, 151–169 (2005). https://doi.org/10.1007/s11118-004-0588-4

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  • DOI: https://doi.org/10.1007/s11118-004-0588-4

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