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Mat. Tr., 2007, Volume 10, Number 2, Pages 187–212 (Mi mt26)  

This article is cited in 1 scientific paper (total in 1 paper)

The Extension of Functions of Sobolev Classes Beyond the Boundary of the Domain on Carnot Groups

I. M. Pupyshev

Novosibirsk State Technical University

Abstract: We prove the theorem on extension of the functions of the Sobolev space $W^l_p(\Omega)$ which are defined on a bounded $(\varepsilon,\delta)$-domain $\Omega$ in a two-step Carnot group beyond the boundary of the domain of definition. This theorem generalizes the well-known extension theorem by P. Jones for domains of the Euclidean space.

Key words: Sobolev space, Carnot group, extension of functions beyond the boundary of the domain of definition.

Full text: PDF file (305 kB)
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English version:
Siberian Advances in Mathematics, 2008, 18:2, 124–141

Bibliographic databases:

UDC: 517.54+517.813.52
Received: 22.12.2006

Citation: I. M. Pupyshev, “The Extension of Functions of Sobolev Classes Beyond the Boundary of the Domain on Carnot Groups”, Mat. Tr., 10:2 (2007), 187–212; Siberian Adv. Math., 18:2 (2008), 124–141

Citation in format AMSBIB
\Bibitem{Pup07}
\by I.~M.~Pupyshev
\paper The Extension of Functions of Sobolev Classes Beyond the Boundary of the~Domain on Carnot Groups
\jour Mat. Tr.
\yr 2007
\vol 10
\issue 2
\pages 187--212
\mathnet{http://mi.mathnet.ru/mt26}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2382422}
\elib{http://elibrary.ru/item.asp?id=9568702}
\transl
\jour Siberian Adv. Math.
\yr 2008
\vol 18
\issue 2
\pages 124--141
\crossref{https://doi.org/10.3103/S1055134408020065}
\elib{http://elibrary.ru/item.asp?id=13566554}


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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
  • Математические труды Siberian Advances in Mathematics
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