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Mat. Zametki, 2003, Volume 74, Issue 2, Pages 163–183 (Mi mz253)  

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

Spaces of Functions of Fractional Smoothness on an Irregular Domain

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 with positive exponent of smoothness $s > 0$, defined on a domain $G\subset\mathbb R^n$. For a domain $G$ with specific geometric properties, we establish the embedding $B_{pp}^s(G)=L_{pp}^s(G)\subset L_q(G)$, $1<p<q<\infty$, with the relationship between the parameters defined by these geometric properties.

DOI: https://doi.org/10.4213/mzm253

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English version:
Mathematical Notes, 2003, 74:2, 157–176

Bibliographic databases:

UDC: 517.518
Received: 11.04.2002
Revised: 10.02.2003

Citation: O. V. Besov, “Spaces of Functions of Fractional Smoothness on an Irregular Domain”, Mat. Zametki, 74:2 (2003), 163–183; Math. Notes, 74:2 (2003), 157–176

Citation in format AMSBIB
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\yr 2003
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\pages 163--183
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\pages 157--176
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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. “The List of Scientific Works of O. V. Besov”, Proc. Steklov Inst. Math., 243 (2003), 7–10  mathnet  mathscinet  zmath
    2. 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
    3. 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
    4. Besov O.V., “Integral estimates for differentiable functions on irregular domains”, Doklady Mathematics, 81:1 (2010), 87–90  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, “Integral estimates for differentiable functions on irregular domains”, Sb. Math., 201:12 (2010), 1777–1790  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. 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
    8. 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  isi  elib
    9. Besov O.V., “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains”, Dokl. Math., 99:1 (2019), 31–35  crossref  isi
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