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Mat. Zametki, 2003, Volume 74, Issue 3, Pages 340–349 (Mi mz267)  

This article is cited in 9 scientific papers (total in 9 papers)

Equivalent Norms in Spaces of Functions of Fractional Smoothness on Arbitrary Domains

O. V. Besov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this paper, we study the spaces $B_{pq}^s(G)$ and $L_{pq}^s(G)$ of functions $f$ with positive exponent of smoothness $s > 0$ given on a domain $G\subset\mathbb R^n$. The norms on these spaces are defined via integral norms of the difference of the function $f$ of order $m > s$ treated as a function of the point of the domain and of the difference increment. For an arbitrary domain $G\subset\mathbb R^n$, we characterize these spaces in terms of the local approximations of the function by polynomials of degree $m-1$.

DOI: https://doi.org/10.4213/mzm267

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English version:
Mathematical Notes, 2003, 74:3, 326–334

Bibliographic databases:

UDC: 517.518
Received: 11.04.2002

Citation: O. V. Besov, “Equivalent Norms in Spaces of Functions of Fractional Smoothness on Arbitrary Domains”, Mat. Zametki, 74:3 (2003), 340–349; Math. Notes, 74:3 (2003), 326–334

Citation in format AMSBIB
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\by O.~V.~Besov
\paper Equivalent Norms in Spaces of Functions of Fractional Smoothness on Arbitrary Domains
\jour Mat. Zametki
\yr 2003
\vol 74
\issue 3
\pages 340--349
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\crossref{https://doi.org/10.4213/mzm267}
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\jour Math. Notes
\yr 2003
\vol 74
\issue 3
\pages 326--334
\crossref{https://doi.org/10.1023/A:1026198500722}
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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, “Spaces of Functions of Fractional Smoothness on an Irregular Domain”, Math. Notes, 74:2 (2003), 157–176  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. “The List of Scientific Works of O. V. Besov”, Proc. Steklov Inst. Math., 243 (2003), 7–10  mathnet  mathscinet  zmath
    3. O. V. Besov, “Function Spaces of Lizorkin–Triebel Type on an Irregular Domain”, Proc. Steklov Inst. Math., 260 (2008), 25–36  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    4. Besov, OV, “Spaces of functions of fractional smoothness on an irregular domain”, Doklady Mathematics, 79:2 (2009), 223  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. 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
    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. Besov O.V., “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687  mathnet  crossref  mathscinet  zmath  isi  scopus
    8. 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
    9. Sawano Y., Theory of Besov Spaces, Developments in Mathematics, 56, Springer International Publishing Ag, 2018  crossref  isi
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