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Sibirsk. Mat. Zh., 2002, Volume 43, Number 4, Pages 864–878 (Mi smj1336)  

This article is cited in 8 scientific papers (total in 8 papers)

On inequalities with measures of Sobolev type embedding theorems on open sets of the real axis

D. V. Prokhorov, V. D. Stepanov

Computer Centre Far-Eastern Branch of RAS

Abstract: We consider some Sobolev-type spaces and obtain a necessary and sufficient condition for their embedding in a Lebesgue space.

Keywords: Sobolev space, weighted Lebesgue space, embedding theorem

Full text: PDF file (258 kB)

English version:
Siberian Mathematical Journal, 2002, 43:4, 694–707

Bibliographic databases:

UDC: 517.51
Received: 21.11.2001

Citation: D. V. Prokhorov, V. D. Stepanov, “On inequalities with measures of Sobolev type embedding theorems on open sets of the real axis”, Sibirsk. Mat. Zh., 43:4 (2002), 864–878; Siberian Math. J., 43:4 (2002), 694–707

Citation in format AMSBIB
\Bibitem{ProSte02}
\by D.~V.~Prokhorov, V.~D.~Stepanov
\paper On inequalities with measures of Sobolev type embedding theorems on open sets of the real axis
\jour Sibirsk. Mat. Zh.
\yr 2002
\vol 43
\issue 4
\pages 864--878
\mathnet{http://mi.mathnet.ru/smj1336}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1934586}
\zmath{https://zbmath.org/?q=an:1053.46021}
\transl
\jour Siberian Math. J.
\yr 2002
\vol 43
\issue 4
\pages 694--707
\crossref{https://doi.org/10.1023/A:1016380420615}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000177460300011}


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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. A. S. Romanov, “Singular measures and $(1,p)$-capacity on weighted Sobolev classes”, Siberian Math. J., 44:2 (2003), 346–349  mathnet  crossref  mathscinet  zmath  isi
    2. Eveson S.P. Stepanov V.D. Ushakova E.P., “a Duality Principle in Weighted Sobolev Spaces on the Real Line”, Math. Nachr., 288:8-9 (2015), 877–897  crossref  mathscinet  zmath  isi  elib  scopus
    3. Oinarov R., Ramazanova Kh., Tiryaki A., “An Extension of the Weighted Hardy Inequalities and Its Application to Half-Linear Equations”, Taiwan. J. Math., 19:6 (2015), 1693–1711  crossref  mathscinet  zmath  isi  scopus
    4. Prokhorov D.V., Stepanov V.D., Ushakova E.P., “on Weighted Sobolev Spaces on the Real Line”, Dokl. Math., 93:1 (2016), 78–81  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    5. D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Integral Operators”, Proc. Steklov Inst. Math., 300, suppl. 2 (2018), 1–112  mathnet  crossref  crossref  zmath  isi  elib
    6. Prokhorov D.V., Stepanov V.D., Ushakova E.P., “on Associate Spaces of Weighted Sobolev Space on the Real Line”, Math. Nachr., 290:5-6 (2017), 890–912  crossref  mathscinet  zmath  isi  scopus
    7. Stepanov V.D., Ushakova E.P., “Hardy-Steklov Operators and Duality Principle in Weighted Sobolev Spaces of the First Order”, Dokl. Math., 97:3 (2018), 232–235  mathnet  crossref  mathscinet  zmath  isi  scopus
    8. D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line”, Russian Math. Surveys, 74:6 (2019), 1075–1115  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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