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This article is cited in 13 scientific papers (total in 13 papers)
Absolute continuity of the Sobolev type functions on metric spaces
A. S. Romanov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
Under study is the absolute continuity of the functions satisfying the Poincaré inequality on $s$-regular metric spaces.
Keywords:
absolute continuity, Lorentz space, Poincaré inequality.
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English version:
Siberian Mathematical Journal, 2008, 49:5, 911–918
Bibliographic databases:
  
UDC:
517.51
Received: 29.12.2007
Citation:
A. S. Romanov, “Absolute continuity of the Sobolev type functions on metric spaces”, Sibirsk. Mat. Zh., 49:5 (2008), 1147–1156; Siberian Math. J., 49:5 (2008), 911–918
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/smj1909 http://mi.mathnet.ru/eng/smj/v49/i5/p1147
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Wildrick K., Zurcher T., “Space filling with metric measure spaces”, Math Z, 270:1–2 (2012), 103–131
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Korobkov M.V., Kristensen J., “on the Morse-Sard Theorem For the Sharp Case of Sobolev Mappings”, Indiana Univ. Math. J., 63:6 (2014), 1703–1724
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Zurcher T., “Space-Filling Vs. Luzin'S Condition (N)”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 39:2 (2014), 831–857
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A. S. Romanov, “O nepreryvnosti sobolevskikh funktsii na giperploskostyakh”, Sib. elektron. matem. izv., 12 (2015), 832–841
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Wildrick K., Zurcher T., “Sharp Differentiability Results For the Lower Local Lipschitz Constant and Applications To Non-Embedding”, J. Geom. Anal., 25:4 (2015), 2590–2616
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Maly L., “Fine Properties of Newtonian Functions and the Sobolev Capacity on Metric Measure Spaces”, Rev. Mat. Iberoam., 32:1 (2016), 219–255
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A. S. Romanov, “O gelderovosti sobolevskikh funktsii na giperpoverkhnostyakh”, Sib. elektron. matem. izv., 13 (2016), 624–634
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Hajlasz P., Korobkov M.V., Kristensen J., “a Bridge Between Dubovitskii-Federer Theorems and the Coarea Formula”, J. Funct. Anal., 272:3 (2017), 1265–1295
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A. S. Romanov, “Absolute continuity of functions in Sobolev spaces and modules of families of hypersurfaces elated to the Lorentz spaces”, J. Math. Sci., 231:2 (2018), 255–266
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Korobkov M.V., Kristensen J., “The Trace Theorem, the Luzin N- and Morse-Sard Properties For the Sharp Case of Sobolev-Lorentz Mappings”, J. Geom. Anal., 28:3 (2018), 2834–2856
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A. Ferone, M. V. Korobkov, A. Roviello, “The Morse–Sard theorem and Luzin $N$-property: a new synthesis for smooth and Sobolev mappings”, Siberian Math. J., 60:5 (2019), 916–926
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Zhou X., “Absolutely Continuous Functions on Compact and Connected 1-Dimensional Metric Spaces”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 44 (2019), 281–291
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Ferone A., Korobkov V M., Roviello A., “on the Luzin N-Property and the Uncertainty Principle For Sobolev Mappings”, Anal. PDE, 12:5 (2019), 1149–1175
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