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Matematicheskie Zametki, 1969, Volume 6, Issue 2, Pages 129–138 (Mi mzm6916)  

This article is cited in 7 scientific papers (total in 7 papers)

An embedding theorem for a limiting exponent

O. V. Besova, V. P. Il'inb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Leningrad Department of V. A. Steklov Institute of Mathematics, USSR Academy of Sciences
Full-text PDF (534 kB) Citations (7)
Abstract: We consider the function space $B_{p,\theta}^l(\Omega)$ of functions $f(x)$, defined on the domain $\Omega$ of a certain class and characterized by specific differential-difference properties in $L_p(\Omega)$. We prove a theorem on the embedding $B_{p,q}^l\subset\Omega)$ in the case when $l=n/p-n/q>0$ and its generalization for vector $l$, $p$, $q$.
Received: 11.11.1968
English version:
Mathematical Notes, 1969, Volume 6, Issue 2, Pages 537–542
DOI: https://doi.org/10.1007/BF01093694
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: O. V. Besov, V. P. Il'in, “An embedding theorem for a limiting exponent”, Mat. Zametki, 6:2 (1969), 129–138; Math. Notes, 6:2 (1969), 537–542
Citation in format AMSBIB
\Bibitem{BesIli69}
\by O.~V.~Besov, V.~P.~Il'in
\paper An embedding theorem for a~limiting exponent
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 2
\pages 129--138
\mathnet{http://mi.mathnet.ru/mzm6916}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=259588}
\zmath{https://zbmath.org/?q=an:0188.43903|0179.17702}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 2
\pages 537--542
\crossref{https://doi.org/10.1007/BF01093694}
Linking options:
  • https://www.mathnet.ru/eng/mzm6916
  • https://www.mathnet.ru/eng/mzm/v6/i2/p129
  • This publication is cited in the following 7 articles:
    1. D. M. Stolyarov, “Hardy-Littlewood-Sobolev inequality for $p=1$”, Sb. Math., 213:6 (2022), 844–889  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Sawano Y., Theory of Besov Spaces, Developments in Mathematics, 56, Springer International Publishing Ag, 2018  crossref  isi
    3. “The List of Scientific Works of O. V. Besov”, Proc. Steklov Inst. Math., 243 (2003), 7–10  mathnet  mathscinet  zmath
    4. V. I. Kolyada, “Rearrangements of functions and embedding theorems”, Russian Math. Surveys, 44:5 (1989), 73–117  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. V. I. Kolyada, “On embedding $H_p^{\omega_1,\dots,\omega_\nu}$ classes”, Math. USSR-Sb., 55:2 (1986), 351–381  mathnet  crossref  mathscinet  zmath
    6. Ya. S. Bugrov, “Imbedding theorems for classes of functions with mixed norm”, Math. USSR-Sb., 21:4 (1973), 607–618  mathnet  crossref  mathscinet  zmath
    7. V. P. Il'in, Automatic Programming and Numerical Methods of Analysis, 1972, 111  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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