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Geometric Interpretations of LP-Poincaré Inequalities on Graphs with Polynomial Volume Growth

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Abstract.

On graphs with polynomial volume growth of exponent Q, we characterize Lp-Poincaré inequalities in the range Q − 1 < p < +∞ in terms of capacity estimates, depending on the position of p with respect to Q.

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Authors and Affiliations

  1. Université de Cergy-Pontoise,  

    Thierry Coulhon

  2. University of Jyväskylä,  

    Pekka Koskela

Authors
  1. Thierry Coulhon
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  2. Pekka Koskela
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Correspondence to Thierry Coulhon.

Additional information

Research partially supported by the European Commission (IHP Network “Harmonic Analysis and Related Problems” 2002–2006, Contract HPRN-CT-2001-00273-HARP).

Lecture held by Th. Coulhon in the Seminario Matematico e Fisico on January 19, 2004

Received: May, 2004

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Coulhon, T., Koskela, P. Geometric Interpretations of LP-Poincaré Inequalities on Graphs with Polynomial Volume Growth. Milan j. math. 72, 209–248 (2004). https://doi.org/10.1007/s00032-004-0027-4

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  • DOI: https://doi.org/10.1007/s00032-004-0027-4

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