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Siberian Mathematical Journal

, Volume 49, Issue 2, pp 339–352 | Cite as

Integral representations and the generalized Poincaré inequality on Carnot groups

  • E. A. PlotnikovaEmail author
Article

Abstract

We give some integral representations of the form f(x) = P(f)+K(∇f) on two-step Carnot groups, where P(f) is a polynomial and K is an integral operator with a specific singularity. We then obtain the weak Poincaré inequality and coercive estimates as well as the generalized Poincaré inequality on the general Carnot groups.

Keywords

Carnot group integral representation Poincaré inequality 

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia

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