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Tr. Mat. Inst. Steklova, 2010, Volume 269, Pages 31–51 (Mi tm2890)  

This article is cited in 6 scientific papers (total in 6 papers)

Spaces of functions of fractional smoothness on an irregular domain

O. V. Besov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: On an irregular domain $G\subset\mathbb R^n$ of a certain type, we introduce spaces of functions of fractional smoothness $s>0$. We prove embedding theorems relating these spaces to the Sobolev spaces $W_p^m(G)$ and Lebesgue spaces $L_p(G)$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 269, 25–45

Bibliographic databases:

UDC: 517.5
Received in October 2009

Citation: O. V. Besov, “Spaces of functions of fractional smoothness on an irregular domain”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Tr. Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 31–51; Proc. Steklov Inst. Math., 269 (2010), 25–45

Citation in format AMSBIB
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\paper Spaces of functions of fractional smoothness on an irregular domain
\inbook Function theory and differential equations
\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2010
\vol 269
\pages 31--51
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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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. O. V. Besov, “Integral estimates for differentiable functions on irregular domains”, Sb. Math., 201:12 (2010), 1777–1790  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Proc. Steklov Inst. Math., 293 (2016), 56–66  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Besov O.V., “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687  mathnet  crossref  mathscinet  zmath  isi  scopus
    4. Besov O.V., “Spaces of functions of positive smoothness on irregular domains”, Dokl. Math., 93:1 (2016), 13–15  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    5. O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Spaces”, Math. Notes, 103:3 (2018), 348–356  mathnet  crossref  crossref  isi  elib
    6. Besov O.V., “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains”, Dokl. Math., 99:1 (2019), 31–35  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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