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Mat. Tr., 2004, Volume 7, Number 1, Pages 13–49 (Mi mt69)  

This article is cited in 18 scientific papers (total in 18 papers)

Set Functions and Their Applications in the Theory of Lebesgue and Sobolev Spaces. II

S. K. Vodop'yanova, A. D.-O. Ukhlovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Khabarovsk State University of Technology

Abstract: We study the properties of the mappings inducing a bounded operator of Lebesgue or Sobolev spaces by change of variable and the properties of the operator of extension of functions in Sobolev classes beyond the domain of definition.

Key words: quasiadditive set function, Lebesgue space, Sobolev space, embedding theorems.

Full text: PDF file (2797 kB)
References: PDF file   HTML file

English version:
Siberian Advances in Mathematics, 2005, 15:1, 91–125

Bibliographic databases:

UDC: 517.518.1+517.54
Received: 02.04.2002

Citation: S. K. Vodop'yanov, A. D.-O. Ukhlov, “Set Functions and Their Applications in the Theory of Lebesgue and Sobolev Spaces. II”, Mat. Tr., 7:1 (2004), 13–49; Siberian Adv. Math., 15:1 (2005), 91–125

Citation in format AMSBIB
\Bibitem{VodUkh04}
\by S.~K.~Vodop'yanov, A.~D.-O.~Ukhlov
\paper Set Functions and Their Applications in the~Theory of Lebesgue and Sobolev Spaces.~II
\jour Mat. Tr.
\yr 2004
\vol 7
\issue 1
\pages 13--49
\mathnet{http://mi.mathnet.ru/mt69}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2068275}
\zmath{https://zbmath.org/?q=an:1091.47027}
\elib{https://elibrary.ru/item.asp?id=9530092}
\transl
\jour Siberian Adv. Math.
\yr 2005
\vol 15
\issue 1
\pages 91--125


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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. Karmanova M., “Geometric measure theory formulas on rectifiable metric spaces”, Interaction of Analysis and Geometry, Contemporary Mathematics Series, 424, 2007, 103–136  crossref  mathscinet  zmath  isi
    2. Reshetnyak Yu.G., “Sobolev-type classes of mappings with values in metric spaces”, Interaction of Analysis and Geometry, Contemporary Mathematics Series, 424, 2007, 209–226  crossref  mathscinet  zmath  isi
    3. Vodopyanov S.K., “Foundations of the theory of mappings with bounded distortion on carnot groups”, Interaction of Analysis and Geometry, Contemporary Mathematics Series, 424, 2007, 303–344  crossref  mathscinet  zmath  isi
    4. Karmanova M., “Rectifiable sets and coarea formula for metric-valued mappings”, J. Funct. Anal., 254:5 (2008), 1410–1447  crossref  mathscinet  zmath  isi  elib  scopus
    5. Ukhlov A., Vodopyanov S.K., “Mappings associated with weighted Sobolev spaces”, Complex Analysis and Dynamical Systems III, Contemporary Mathematics Series, 455, 2008, 369–382  crossref  mathscinet  zmath  isi
    6. Gol'dshtein V., Ukhlov A., “Weighted Sobolev spaces and embedding theorems”, Trans. Amer. Math. Soc., 361:7 (2009), 3829–3850  crossref  mathscinet  zmath  isi  scopus
    7. Karmanova M., Vodop'yanov S., “Geometry of Carnot-Caratheodory Spaces, Differentiability, Coarea and Area Formulas”, Analysis and Mathematical Physics, Trends in Mathematics, 2009, 233–335  mathscinet  zmath  isi
    8. Ukhlov A., Vodop'yanov S.K., “Mappings with bounded (P, Q)-distortion on Carnot groups”, Bull Sci Math, 134:6 (2010), 605–634  crossref  mathscinet  zmath  isi  elib  scopus
    9. Ukhlov A., “Composition operators in weighted Sobolev spaces on Carnot groups”, Acta Math Hungar, 133:1–2 (2011), 103–127  crossref  mathscinet  zmath  isi  elib  scopus
    10. M. B. Karmanova, “The graphs of Lipschitz functions and minimal surfaces on Carnot groups”, Siberian Math. J., 53:4 (2012), 672–690  mathnet  crossref  mathscinet  isi
    11. Karmanova M. Vodopyanov S., “A Coarea Formula for Smooth Contact Mappings of Carnot-Carath,Odory Spaces”, Acta Appl. Math., 128:1 (2013), 67–111  crossref  mathscinet  zmath  isi  elib  scopus
    12. M. B. Karmanova, “The area formula for graphs on $4$-dimensional $2$-step sub-Lorentzian structures”, Siberian Math. J., 56:5 (2015), 852–871  mathnet  crossref  crossref  isi  elib  elib
    13. M. B. Karmanova, “Graph surfaces over three-dimensional Lie groups with sub-Riemannian structure”, Siberian Math. J., 56:6 (2015), 1080–1092  mathnet  crossref  crossref  mathscinet  isi  elib
    14. A. V. Menovshchikov, “Composition operators in Orlicz–Sobolev spaces”, Siberian Math. J., 57:5 (2016), 849–859  mathnet  crossref  crossref  isi  elib  elib
    15. M. B. Karmanova, “Graph surfaces on five-dimensional sub-Lorentzian structures”, Siberian Math. J., 58:1 (2017), 91–108  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. M. B. Karmanova, “Area formulas for classes of Hölder continuous mappings of Carnot groups”, Siberian Math. J., 58:5 (2017), 817–836  mathnet  crossref  crossref  isi  elib  elib
    17. M. B. Karmanova, “Three-dimensional graph surfaces on five-dimensional Carnot–Carathéodory spaces”, Siberian Math. J., 59:4 (2018), 657–676  mathnet  crossref  crossref  isi  elib
    18. M. B. Karmanova, “Two-step sub-Lorentzian structures and graph surfaces”, Izv. Math., 84:1 (2020), 52–94  mathnet  crossref  crossref  isi  elib
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