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Mat. Zametki, 1977, Volume 22, Issue 2, Pages 297–301 (Mi mz8050)  

This article is cited in 1 scientific paper (total in 1 paper)

Theorems on imbedding in anisotropic spaces of vector-valued functions

S. Ya. Yakubova, V. B. Shakhmurovb

a Institute of Applied Mathematics and Mechanics AS of AzSSR
b Azerbaijan Pedagogical Institute

Abstract: Imbedding theorems are proved for abstract anisotropic spaces of Sobolev type. In particular, it is proved that if $G$ is a bounded set satisfying the $l$ horn condition, then there holds the imbedding
$$ D^\alpha W_2(G;H(A),H)\hookrightarrow L_2(G;H(A^1-|\alpha:l|)), $$
where $|\alpha:l|=\frac{\alpha_1}{l_2}+…+\frac{\alpha_n}{l_n}\le1$, $H$ is a Hilbert space, and $A$ is a self-adjoint positive operator.

Full text: PDF file (295 kB)

English version:
Mathematical Notes, 1977, 22:2, 657–659

Bibliographic databases:

UDC: 517.5
Received: 03.06.1976

Citation: S. Ya. Yakubov, V. B. Shakhmurov, “Theorems on imbedding in anisotropic spaces of vector-valued functions”, Mat. Zametki, 22:2 (1977), 297–301; Math. Notes, 22:2 (1977), 657–659

Citation in format AMSBIB
\Bibitem{YakSha77}
\by S.~Ya.~Yakubov, V.~B.~Shakhmurov
\paper Theorems on imbedding in anisotropic spaces of vector-valued functions
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 297--301
\mathnet{http://mi.mathnet.ru/mz8050}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=477740}
\zmath{https://zbmath.org/?q=an:0359.46023}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 657--659
\crossref{https://doi.org/10.1007/BF01780977}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. B. Shakhmurov, “Imbedding theorems for abstract function spaces and their applications”, Math. USSR-Sb., 62:1 (1989), 261–276  mathnet  crossref  mathscinet  zmath
  • Математические заметки Mathematical Notes
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