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Mat. Tr., 2010, Volume 13, Number 2, Pages 139–178 (Mi mt202)  

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

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

A. I. Parfenov

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

Abstract: We obtain two new equivalent quasinorms for unweighted isotropic Besov and Lizorkin–Triebel spaces in the epigraph of a Lipschitz function. The question on the straightening is studied, i. e., the question on the existence of a diffeomorphism taking the epigraph into a halfspace which preserves the Lizorkin–Triebel spaces of the same indices. A criterion for the straightening is established in terms of dyadic weighted inequality where oscillations of a given function on stretched dyadic cubes are involved.

Key words: Lipschitz domain, composition operator, superposition operator, Besov space, Lizorkin-Triebel space, straightening.

Full text: PDF file (428 kB)
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English version:
Siberian Advances in Mathematics, 2011, 21:2, 100–129

Bibliographic databases:

Document Type: Article
UDC: 517.518.234
Received: 17.12.2009

Citation: A. I. Parfenov, “A criterion for straightening a Lipschitz surface in the Lizorkin–Triebel sense. III”, Mat. Tr., 13:2 (2010), 139–178; Siberian Adv. Math., 21:2 (2011), 100–129

Citation in format AMSBIB
\Bibitem{Par10}
\by A.~I.~Parfenov
\paper A criterion for straightening a~Lipschitz surface in the Lizorkin--Triebel sense.~III
\jour Mat. Tr.
\yr 2010
\vol 13
\issue 2
\pages 139--178
\mathnet{http://mi.mathnet.ru/mt202}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2789959}
\transl
\jour Siberian Adv. Math.
\yr 2011
\vol 21
\issue 2
\pages 100--129
\crossref{https://doi.org/10.3103/S1055134411020027}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. A. I. Parfenov, “A characterization of multipliers in the Hedberg–Netrusov spaces”, Siberian Adv. Math., 22:1 (2012), 13–40  mathnet  crossref  mathscinet  elib
    2. A. I. Parfënov, “Vesovaya apriornaya otsenka v raspryamlyaemykh oblastyakh lokalnogo tipa Lyapunova–Dini”, Sib. elektron. matem. izv., 9 (2012), 65–150  mathnet
    3. A. I. Parfënov, “Otsenka pogreshnosti obobschennoi formuly M. A. Lavrenteva normoi drobnogo prostranstva Soboleva”, Sib. elektron. matem. izv., 10 (2013), 335–377  mathnet
    4. A. I. Parfenov, “Dicrete Hölder estimates for a certain kind of parametrix. II”, Ufa Math. J., 9:2 (2017), 62–91  mathnet  crossref  isi  elib
  • Математические труды Siberian Advances in Mathematics
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