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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.
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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
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\jour Mat. Tr.
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\vol 7
\issue 1
\pages 13--49
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\transl
\jour Siberian Adv. Math.
\yr 2005
\vol 15
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\pages 91--125
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http://mi.mathnet.ru/eng/mt69 http://mi.mathnet.ru/eng/mt/v7/i1/p13
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Karmanova M., “Rectifiable sets and coarea formula for metric-valued mappings”, J. Funct. Anal., 254:5 (2008), 1410–1447
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Ukhlov A., Vodopyanov S.K., “Mappings associated with weighted Sobolev spaces”, Complex Analysis and Dynamical Systems III, Contemporary Mathematics Series, 455, 2008, 369–382
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Gol'dshtein V., Ukhlov A., “Weighted Sobolev spaces and embedding theorems”, Trans. Amer. Math. Soc., 361:7 (2009), 3829–3850
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Karmanova M. Vodopyanov S., “A Coarea Formula for Smooth Contact Mappings of Carnot-Carath,Odory Spaces”, Acta Appl. Math., 128:1 (2013), 67–111
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