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

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

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
\Bibitem{Sha08} \by V.~B.~Shakhmurov \paper Embeddings and Separable Differential Operators in Spaces of Sobolev--Lions type \jour Mat. Zametki \yr 2008 \vol 84 \issue 6 \pages 907--926 \mathnet{http://mi.mathnet.ru/mz6567} \crossref{https://doi.org/10.4213/mzm6567} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2492805} \transl \jour Math. Notes \yr 2008 \vol 84 \issue 6 \pages 842--858 \crossref{https://doi.org/10.1134/S0001434608110278} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000262855600027} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-59749091391} 

• http://mi.mathnet.ru/eng/mz6567
• https://doi.org/10.4213/mzm6567
• http://mi.mathnet.ru/eng/mz/v84/i6/p907

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