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Trudy Mat. Inst. Steklova, 2008, Volume 260, Pages 32–43 (Mi tm584)  

This article is cited in 14 scientific papers (total in 14 papers)

Function Spaces of Lizorkin–Triebel Type on an Irregular Domain

O. V. Besov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: On an irregular domain $G\subset\mathbb R^n$ of a certain type, we introduce function spaces of fractional smoothness $s>0$ that are similar to the Lizorkin–Triebel spaces. We prove embedding theorems that show how these spaces are related to the Sobolev and Lebesgue spaces $W_p^m(G)$ and $L_p(G)$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 260, 25–36

Bibliographic databases:

UDC: 517.5
Received in November 2007

Citation: O. V. Besov, “Function Spaces of Lizorkin–Triebel Type on an Irregular Domain”, Function theory and nonlinear partial differential equations, Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 260, MAIK Nauka/Interperiodica, Moscow, 2008, 32–43; Proc. Steklov Inst. Math., 260 (2008), 25–36

Citation in format AMSBIB
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\by O.~V.~Besov
\paper Function Spaces of Lizorkin--Triebel Type on an Irregular Domain
\inbook Function theory and nonlinear partial differential equations
\bookinfo Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2008
\vol 260
\pages 32--43
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2008
\vol 260
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\crossref{https://doi.org/10.1134/S0081543808010033}
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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. Besov O.V., “Function spaces of Lizorkin-Triebel type on an irregular domain”, Nonlinear Anal., 70:8 (2009), 2842–2845  crossref  mathscinet  zmath  isi  elib  scopus
    2. Besov O.V., “Spaces of functions of fractional smoothness on an irregular domain”, Dokl. Math., 79:2 (2009), 223–226  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Besov O.V., “Integral estimates for differentiable functions on irregular domains”, Dokl. Math., 81:1 (2010), 87–90  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. O. V. Besov, “Spaces of functions of fractional smoothness on an irregular domain”, Proc. Steklov Inst. Math., 269 (2010), 25–45  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. 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
    6. 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
    7. Hans Triebel, “A note on function spaces in rough domains”, Proc. Steklov Inst. Math., 293 (2016), 338–342  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Besov O.V., “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687  mathnet  crossref  mathscinet  zmath  isi  scopus
    9. 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
    10. O. V. Besov, “Another Note on the Embedding of the Sobolev Space for the Limiting Exponent”, Math. Notes, 101:4 (2017), 608–618  mathnet  crossref  crossref  mathscinet  isi  elib
    11. 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  mathscinet  isi  elib
    12. O. V. Besov, “Embeddings of Weighted Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Space”, Math. Notes, 104:6 (2018), 799–809  mathnet  crossref  crossref  mathscinet  isi  elib
    13. Besov O.V., “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains”, Dokl. Math., 99:1 (2019), 31–35  crossref  isi
    14. O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains”, Math. Notes, 106:4 (2019), 501–513  mathnet  crossref  crossref  mathscinet  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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