Separable anisotropic differential operators in weighted abstract spaces and applications

DOI10.1016/j.jmaa.2007.05.078zbMath1138.47037OpenAlexW1973178346MaRDI QIDQ2473951

Veli B. Shakhmurov, Ravi P. Agarwal, Donal O'Regan

Publication date: 5 March 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.05.078

zbMATH Keywords

boundary value problemspositive operatorsUMD spacesoperator-valued multipliersinterpolation of Banach spacesdifferential-operator equationsBanach space-valued functions\(R\)-bounded sets

Mathematics Subject Classification ID

Multipliers for harmonic analysis in several variables (42B15) General theory of partial differential operators (47F05) Applications of operator theory to differential and integral equations (47N20) Applications of functional analysis to differential and integral equations (46N20)

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Cites Work

• Unnamed Item
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• Unnamed Item
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• Some remarks on Banach spaces in which martingale difference sequences are unconditional
• Equations d'évolution linéaires associées à des semi-groupes de contractions dans les espaces \(L^ p\). (Evolution equations associated to contraction semigroups in \(L^ p\) spaces)
• On the closedness of the sum of two closed operators
• Coercive boundary value problems for regular degenerate differential-operator equations
• Embedding operators and maximal regular differential-operator equations in Banach-valued function spaces
• Sur les multiplicateurs dans \({\mathcal F}L^ p\) avec poids
• On a class of interpolation spaces
• Maximal regular boundary value problems in Banach-valued weighted space
• On Fourier Multiplier Transformations of Banach-Valued Functions
• IMBEDDING THEOREMS FOR ABSTRACT FUNCTION SPACES AND THEIR APPLICATIONS
• Spaces of Distributions with Weights. Multipliers inLp-spaces with Weights
• On vector-valued Fourier multiplier theorems
• Operator-Valued Fourier Multipliers, Vector - Valued Besov Spaces, and Applications
• Heat kernels and maximal l^p—l^qestimates for parabolic evolution equations
• ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
• Hardy's inequality with weights
• Properties of solutions of ordinary differential equations in banach space
• Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity
• Complete second order linear differential equations in Hilbert spaces