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Sibirsk. Mat. Zh., 2008, Volume 49, Number 2, Pages 420–436 (Mi smj1850)  

This article is cited in 4 scientific papers (total in 4 papers)

Integral representations and the generalized Poincaré inequality on Carnot groups

E. A. Plotnikova

Novosibirsk State University, Mechanics and Mathematics Department

Abstract: We give some integral representations of the form $f(x)=P(f)+K(\nabla f)$ 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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English version:
Siberian Mathematical Journal, 2008, 49:2, 339–352

Bibliographic databases:

UDC: 517.518.23+512.81
Received: 05.06.2007

Citation: E. A. Plotnikova, “Integral representations and the generalized Poincaré inequality on Carnot groups”, Sibirsk. Mat. Zh., 49:2 (2008), 420–436; Siberian Math. J., 49:2 (2008), 339–352

Citation in format AMSBIB
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\by E.~A.~Plotnikova
\paper Integral representations and the generalized Poincaré inequality on Carnot groups
\jour Sibirsk. Mat. Zh.
\yr 2008
\vol 49
\issue 2
\pages 420--436
\mathnet{http://mi.mathnet.ru/smj1850}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2419665}
\zmath{https://zbmath.org/?q=an:1164.46324}
\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 2
\pages 339--352
\crossref{https://doi.org/10.1007/s11202-008-0033-9}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-43349089435}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. K. Vodop'yanov, I. M. Pupyshev, “Traces of Sobolev functions on the Ahlfors sets of Carnot groups”, Siberian Math. J., 48:6 (2007), 961–978  mathnet  crossref  mathscinet  zmath  isi
    2. D. V. Isangulova, S. K. Vodopyanov, “Coercive estimates and integral representation formulas on Carnot groups”, Eurasian Math. J., 1:3 (2010), 58–96  mathnet  mathscinet  zmath
    3. Vodopyanov S.K., Isangulova D.V., “Coercive estimates and integral representation formulas on Carnot groups”, Dokl. Math., 83:3 (2011), 293–297  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. V. A. Markasheva, A. F. Tedeev, “The Cauchy problem for a quasilinear parabolic equation with gradient absorption”, Sb. Math., 203:4 (2012), 581–611  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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