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Mat. Zametki, 2008, Volume 84, Issue 6, Pages 907–926 (Mi mz6567)  

This article is cited in 10 scientific papers (total in 10 papers)

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

V. B. Shakhmurov

Okan University

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 $\alpha=(\alpha_1,\alpha_2,…,\alpha_n)$ and $l=(l_1,l_2,…,l_n)$. The results obtained are applied to prove the separability of anisotropic differential operator equations with variable coefficients.

DOI: https://doi.org/10.4213/mzm6567

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English version:
Mathematical Notes, 2008, 84:6, 842–858

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
Received: 02.09.2005

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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\jour Mat. Zametki
\yr 2008
\vol 84
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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, “Maximal regular abstract elliptic equations and applications”, Siberian Math. J., 51:5 (2010), 935–948  mathnet  crossref  mathscinet  isi  elib
    2. Shakhmurov V.B., “Separable anisotropic elliptic operators and applications”, Acta Math. Hungar., 131:3 (2011), 208–229  crossref  mathscinet  zmath  isi  scopus
    3. Shakhmurov V., “Abstract capacity of regions and compact embedding with applications”, Acta Math. Sci. Ser. B Engl. Ed., 31:1 (2011), 49–67  crossref  mathscinet  zmath  isi  scopus
    4. Gusev N.A., “Asymptotic properties of linearized equations of low compressible fluid motion”, J. Math. Fluid Mech., 14:3 (2012), 591–618  crossref  mathscinet  zmath  isi  elib  scopus
    5. Ragusa M.A., “Embeddings for Morrey-Lorentz spaces”, J. Optim. Theory Appl., 154:2 (2012), 491–499  crossref  mathscinet  zmath  isi  scopus
    6. Shakhmurov V.B., Ekincioglu I., “Linear and Nonlinear Convolution Elliptic Equations”, Bound. Value Probl., 2013  crossref  mathscinet  isi  scopus
    7. Shakhmurov V.B., “Nonlocal problems for Boussinesq equations”, Nonlinear Anal.-Theory Methods Appl., 142 (2016), 134–151  crossref  mathscinet  zmath  isi  scopus
    8. Shakhmurov V., “Abstract Differential Equations with VMO Coefficients in Half Space and Applications”, Mediterr. J. Math., 13:4 (2016), 1765–1785  crossref  mathscinet  zmath  isi  elib  scopus
    9. Shakhmurov V.B., “the Cauchy Problem For Generalized Abstract Boussinesq Equations”, Dyn. Syst. Appl., 25:1-2 (2016), 109–122  mathscinet  zmath  isi  elib
    10. Shakhmurov V., “Regularity Properties of Schrodinger Equations in Vector-Valued Spaces and Applications”, Forum Math., 31:1 (2019), 149–166  crossref  mathscinet  isi  scopus
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