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

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Matematicheskie Trudy, 2004, Volume 7, Number 1, Pages 13–49 (Mi mt69)

This article is cited in 27 scientific papers (total in 27 papers)

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

S. K. Vodop'yanov^a, A. D.-O. Ukhlov^b

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

Full-text PDF (2797 kB) Citations (27)

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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.

Received: 02.04.2002

Bibliographic databases:

UDC: 517.518.1+517.54

Language: Russian

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

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

\jour Mat. Tr.

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\issue 1

\pages 13--49

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2068275}

\zmath{https://zbmath.org/?q=an:1091.47027}

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\transl

\jour Siberian Adv. Math.

\yr 2005

\vol 15

\issue 1

\pages 91--125

Linking options:

https://www.mathnet.ru/eng/mt69

https://www.mathnet.ru/eng/mt/v7/i1/p13

Cycle of papers

Set Functions and Their Applications in the Theory of Lebesgue and Sobolev Spaces. I
S. K. Vodop'yanov, A. D.-O. Ukhlov
Mat. Tr., 2003, 6:2, 14–65
Set Functions and Their Applications in the Theory of Lebesgue and Sobolev Spaces. II
S. K. Vodop'yanov, A. D.-O. Ukhlov
Mat. Tr., 2004, 7:1, 13–49

This publication is cited in the following 27 articles:

M. B. Karmanova, “Ploschad obrazov klassov izmerimykh mnozhestv na gruppakh Karno s sublorentsevoi strukturoi”, Sib. matem. zhurn., 65:5 (2024), 926–952
M. B. Karmanova, “Metric characteristics of classes of compact sets on Carnot groups with sub-Lorentzian structure”, Vladikavk. matem. zhurn., 26:3 (2024), 56–64
S. K. Vodopyanov, “Composition operators in Sobolev spaces on Riemannian manifolds”, Siberian Math. J., 65:6 (2024), 1305–1326
M. B. Karmanova, “Area of images of measurable sets on depth 2 Carnot manifolds with sub-Lorentzian structure”, Vladikavk. matem. zhurn., 26:4 (2024), 78–86
M. B. Karmanova, “Klassy nekontaktnykh otobrazhenii grupp Karno i metricheskie svoistva”, Sib. matem. zhurn., 64:6 (2023), 1199–1223
M. B. Karmanova, “Lipschitz images of open sets on sub-Lorentzian structures”, Siberian Adv. Math., 34:1 (2024), 67–79
M. B. Karmanova, “Sub-Lorentzian coarea formula for mappings of Carnot groups”, Siberian Math. J., 63:3 (2022), 485–508
M. B. Karmanova, “Sub-riemannian properties of the level sets of noncontact mappings of Heisenberg groups”, Siberian Adv. Math., 33:1 (2023), 28–38
M. B. Karmanova, “The coarea formula for vector functions on Carnot groups with sub-Lorentzian structure”, Siberian Math. J., 62:2 (2021), 239–261
M. B. Karmanova, “Two-step sub-Lorentzian structures and graph surfaces”, Izv. Math., 84:1 (2020), 52–94
M. B. Karmanova, “Three-dimensional graph surfaces on five-dimensional Carnot–Carathéodory spaces”, Siberian Math. J., 59:4 (2018), 657–676
M. B. Karmanova, “Graph surfaces on five-dimensional sub-Lorentzian structures”, Siberian Math. J., 58:1 (2017), 91–108
M. B. Karmanova, “Area formulas for classes of Hölder continuous mappings of Carnot groups”, Siberian Math. J., 58:5 (2017), 817–836
A. V. Menovshchikov, “Composition operators in Orlicz–Sobolev spaces”, Siberian Math. J., 57:5 (2016), 849–859
M. B. Karmanova, “The area formula for graphs on $4$ -dimensional $2$ -step sub-Lorentzian structures”, Siberian Math. J., 56:5 (2015), 852–871
M. B. Karmanova, “Graph surfaces over three-dimensional Lie groups with sub-Riemannian structure”, Siberian Math. J., 56:6 (2015), 1080–1092
Karmanova M. Vodopyanov S., “A Coarea Formula for Smooth Contact Mappings of Carnot-Carath,Odory Spaces”, Acta Appl. Math., 128:1 (2013), 67–111
M. B. Karmanova, “The graphs of Lipschitz functions and minimal surfaces on Carnot groups”, Siberian Math. J., 53:4 (2012), 672–690
Ukhlov A., “Composition operators in weighted Sobolev spaces on Carnot groups”, Acta Math Hungar, 133:1–2 (2011), 103–127
Ukhlov A., Vodop'yanov S.K., “Mappings with bounded (P, Q)-distortion on Carnot groups”, Bull Sci Math, 134:6 (2010), 605–634

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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