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Matematicheskie Zametki, 2008, Volume 84, Issue 6, Pages 907–926
DOI: https://doi.org/10.4213/mzm6567
(Mi mzm6567)
 

This article is cited in 23 scientific papers (total in 23 papers)

Embeddings and Separable Differential Operators in Spaces of Sobolev–Lions type

V. B. Shakhmurov

Okan University
References:
Abstract: We study embedding theorems for anisotropic spaces of Bessel–Lions type $H_{p,\gamma}^l(\Omega;E_0,E)$, where $E_0$ and $E$ are Banach spaces. We obtain the most regular spaces $E_\alpha$ for which mixed differentiation operators $D^\alpha$ from $H_{p,\gamma}^l(\Omega;E_0,E)$ to $L_{p,\gamma}(\Omega;E_\alpha)$ are bounded. The spaces $E_\alpha$ are interpolation spaces between $E_0$ and $E$, depending on $\alpha=(\alpha_1,\alpha_2,\dots,\alpha_n)$ and $l=(l_1,l_2,\dots,l_n)$. The results obtained are applied to prove the separability of anisotropic differential operator equations with variable coefficients.
Received: 02.09.2005
English version:
Mathematical Notes, 2008, Volume 84, Issue 6, Pages 842–858
DOI: https://doi.org/10.1134/S0001434608110278
Bibliographic databases:
UDC: embedding operator, Hilbert space, Banach-valued function space, differential operator equation, operator-valued Fourier multiplier, interpolation of Banach spaces, probability space, UMD-space, Sobolev--Lions space
Language: Russian
Citation: V. B. Shakhmurov, “Embeddings and Separable Differential Operators in Spaces of Sobolev–Lions type”, Mat. Zametki, 84:6 (2008), 907–926; Math. Notes, 84:6 (2008), 842–858
Citation in format AMSBIB
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\paper Embeddings and Separable Differential Operators in Spaces of Sobolev--Lions type
\jour Mat. Zametki
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\vol 84
\issue 6
\pages 907--926
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\jour Math. Notes
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  • https://doi.org/10.4213/mzm6567
  • https://www.mathnet.ru/eng/mzm/v84/i6/p907
  • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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