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Mat. Tr., 2009, Volume 12, Number 1, Pages 144–204 (Mi mt178)  

This article is cited in 6 scientific papers (total in 6 papers)

A criterion for straightening of a Lipschitz surface in the Lizorkin–Triebel sense. I

A. I. Parfenov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: We study the conditions when the trace of a Lizorkin–Triebel space on a Lipschitz surface coincides with the trace of this space on a hyperplane. A criterion in terms of a dyadic weighted inequality is found for a wide range of indices.

Key words: Lipschitz domain, dyadic cube, trace, straightening, Lizorkin–Triebel space.

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English version:
Siberian Advances in Mathematics, 2010, 20:2, 83–127

Bibliographic databases:

UDC: 517.518.234
Received: 08.05.2008

Citation: A. I. Parfenov, “A criterion for straightening of a Lipschitz surface in the Lizorkin–Triebel sense. I”, Mat. Tr., 12:1 (2009), 144–204; Siberian Adv. Math., 20:2 (2010), 83–127

Citation in format AMSBIB
\Bibitem{Par09}
\by A.~I.~Parfenov
\paper A criterion for straightening of a~Lipschitz surface in the Lizorkin--Triebel sense.~I
\jour Mat. Tr.
\yr 2009
\vol 12
\issue 1
\pages 144--204
\mathnet{http://mi.mathnet.ru/mt178}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2569651}
\transl
\jour Siberian Adv. Math.
\yr 2010
\vol 20
\issue 2
\pages 83--127
\crossref{https://doi.org/10.3103/S1055134410020021}


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    Cycle of papers

    This publication is cited in the following articles:
    1. A. I. Parfenov, “A criterion for the straightening of a Lipschitz surface in the Lizorkin–Triebel sense. II”, Siberian Adv. Math., 20:3 (2010), 201–216  mathnet  crossref  mathscinet
    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. A. I. Parfenov, “A criterion for straightening a Lipschitz surface in the Lizorkin–Triebel sense. III”, Siberian Adv. Math., 21:2 (2011), 100–129  mathnet  crossref  mathscinet
    4. A. I. Parfenov, “A characterization of multipliers in the Hedberg–Netrusov spaces”, Siberian Adv. Math., 22:1 (2012), 13–40  mathnet  crossref  mathscinet  elib
    5. A. I. Parfënov, “Vesovaya apriornaya otsenka v raspryamlyaemykh oblastyakh lokalnogo tipa Lyapunova–Dini”, Sib. elektron. matem. izv., 9 (2012), 65–150  mathnet
    6. A. I. Parfënov, “Otsenka pogreshnosti obobschennoi formuly M. A. Lavrenteva normoi drobnogo prostranstva Soboleva”, Sib. elektron. matem. izv., 10 (2013), 335–377  mathnet
  • Математические труды Siberian Advances in Mathematics
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