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Mat. Tr., 2007, Volume 10, Number 2, Pages 19–61 (Mi mt20)  

This article is cited in 2 scientific papers (total in 2 papers)

The Traces of Bessel Potentials on Regular Subsets of Carnot Groups

S. K. Vodop'yanova, I. M. Pupyshevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State Technical University

Abstract: We prove the direct theorem on the traces of the Bessel potentials $L^\alpha_p$ defined on a Carnot group, on the regular closed subsets called Ahlfors $d$-sets. The result is convertible for integer $\alpha$, i.e., for the Sobolev spaces $W^\alpha_p$ (the converse trace theorem was proven in [1]). This theorem generalizes A. Johnsson and H. Wallin's results [2] for Sobolev functions and Bessel potentials on the Euclidean space.

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English version:
Siberian Advances in Mathematics, 2008, 18:1, 44–75

Bibliographic databases:

UDC: 517.54:517.813.52
Received: 14.02.2007

Citation: S. K. Vodop'yanov, I. M. Pupyshev, “The Traces of Bessel Potentials on Regular Subsets of Carnot Groups”, Mat. Tr., 10:2 (2007), 19–61; Siberian Adv. Math., 18:1 (2008), 44–75

Citation in format AMSBIB
\Bibitem{VodPup07}
\by S.~K.~Vodop'yanov, I.~M.~Pupyshev
\paper The Traces of Bessel Potentials on Regular Subsets of Carnot Groups
\jour Mat. Tr.
\yr 2007
\vol 10
\issue 2
\pages 19--61
\mathnet{http://mi.mathnet.ru/mt20}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2382416}
\transl
\jour Siberian Adv. Math.
\yr 2008
\vol 18
\issue 1
\pages 44--75
\crossref{https://doi.org/10.3103/S1055134408010045}


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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. S. K. Vodop'yanov, N. A. Kudryavtseva, “Nonlinear potential theory for Sobolev spaces on Carnot groups”, Siberian Math. J., 50:5 (2009), 803–819  mathnet  crossref  mathscinet  isi  elib
  • Математические труды Siberian Advances in Mathematics
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