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Matematicheskie Trudy, 2008, Volume 11, Number 1, Pages 113–131 (Mi mt119)  
This article is cited in 1 scientific paper (total in 1 paper)

Sobolev-type integral representations for functions defined on Carnot groups

E. A. Plotnikova

Novosibirsk State University
Full-text PDF (249 kB) Citations (1)
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Abstract: We obtain some integral representations of the form $f(x)=P(f)+K(\nabla f)$ on the Carnot groups, where $P(f)$ is a polynomial and $K$ is an integral operator with a specific singularity. These representations are employed to prove the weak Poincaré inequality.
Key words: Carnot group, integral representation, Poincaré inequality.
Received: 19.04.2007
English version:
Siberian Advances in Mathematics, 2008, Volume 18, Issue 4, Pages 275–287
DOI: https://doi.org/10.3103/S1055134408040044
Bibliographic databases:
UDC: 517.518.23+517.954
Language: Russian
Citation: E. A. Plotnikova, “Sobolev-type integral representations for functions defined on Carnot groups”, Mat. Tr., 11:1 (2008), 113–131; Siberian Adv. Math., 18:4 (2008), 275–287
Citation in format AMSBIB
\Bibitem{Plo08}
\by E.~A.~Plotnikova
\paper Sobolev-type integral representations for functions defined on Carnot groups
\jour Mat. Tr.
\yr 2008
\vol 11
\issue 1
\pages 113--131
\mathnet{http://mi.mathnet.ru/mt119}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2437484}
\transl
\jour Siberian Adv. Math.
\yr 2008
\vol 18
\issue 4
\pages 275--287
\crossref{https://doi.org/10.3103/S1055134408040044}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    References:65
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