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Sibirsk. Mat. Zh., 2008, Volume 49, Number 5, Pages 1147–1156 (Mi smj1909)  

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.

Full text: PDF file (310 kB)
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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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\by A.~S.~Romanov
\paper Absolute continuity of the Sobolev type functions on metric spaces
\jour Sibirsk. Mat. Zh.
\yr 2008
\vol 49
\issue 5
\pages 1147--1156
\mathnet{http://mi.mathnet.ru/smj1909}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2469060}
\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 5
\pages 911--918
\crossref{https://doi.org/10.1007/s11202-008-0089-6}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-53649110862}


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

    This publication is cited in the following articles:
    1. Wildrick K., Zurcher T., “Space filling with metric measure spaces”, Math Z, 270:1–2 (2012), 103–131  crossref  mathscinet  zmath  isi  scopus
    2. 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  crossref  mathscinet  zmath  isi  elib
    3. Zurcher T., “Space-Filling Vs. Luzin'S Condition (N)”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 39:2 (2014), 831–857  crossref  mathscinet  zmath  isi  scopus
    4. A. S. Romanov, “O nepreryvnosti sobolevskikh funktsii na giperploskostyakh”, Sib. elektron. matem. izv., 12 (2015), 832–841  mathnet  crossref
    5. 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  crossref  mathscinet  zmath  isi  elib  scopus
    6. Maly L., “Fine Properties of Newtonian Functions and the Sobolev Capacity on Metric Measure Spaces”, Rev. Mat. Iberoam., 32:1 (2016), 219–255  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. S. Romanov, “O gelderovosti sobolevskikh funktsii na giperpoverkhnostyakh”, Sib. elektron. matem. izv., 13 (2016), 624–634  mathnet  crossref
    8. 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  crossref  mathscinet  zmath  isi  scopus
    9. 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  mathnet  crossref  crossref
    10. 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  crossref  mathscinet  zmath  isi  scopus
    11. 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  mathnet  crossref  crossref  isi  elib
    12. Zhou X., “Absolutely Continuous Functions on Compact and Connected 1-Dimensional Metric Spaces”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 44 (2019), 281–291  crossref  mathscinet  zmath  isi  scopus
    13. 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  crossref  mathscinet  zmath  isi  scopus
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