R-boundedness, Fourier multipliers, and problems of elliptic and parabollic type.

Intro -- Contents -- Introduction -- Notations and Conventions -- I: R-Boundedness and Sectorial Operators -- 1 Sectorial Operators -- 1.1 Sectorial Operators -- 1.2 Permanence Properties -- 1.3 Perturbation Theory -- 1.4 Dunford Functional Calculus -- 2 The Classes BIP(X) and H[sup(∞)](X) -- 2.1 Extended Functional Calculus -- 2.2 Fractional Powers of Sectorial Operators -- 2.3 Operators with Bounded Imaginary Powers -- 2.4 Operators with Bounded H[sup(∞)]-Calculus -- 3 R-Bounded Families of Operators -- 3.1 R-Bounded Families of Operators -- 3.2 Unconditional Schauder Decompositions -- 3.3 Operator-Valued Fourier Multipliers: One Variable -- 3.4 Fourier Multipliers: Several Variables -- 4 R-Sectorial Operators and Maximal L[sub(p)]-Regularity -- 4.1 R-Sectorial Operators -- 4.2 R-Sectorial Operators and Maximal L[sub(p)]-Regularity -- 4.3 Sufficient Conditions -- 4.4 Operators with R-Bounded Functional Calculus -- 4.5 Further Sufficient Conditions for R-Boundedness -- II: Elliptic and Parabolic Boundary Value Problems -- 5 Elliptic Differential Operators in L[sub(p)](R[sup(n)] -- E) -- 5.1 Kernel Estimates -- 5.2 H[sup(∞)]-Calculus for Elliptic Operators -- 5.3 Elliptic Operators with Variable Coefficients -- 6 Elliptic Problems in a Half Space: General Banach Spaces -- 6.1 Partial Fourier Transforms -- 6.2 The Lopatinskii-Shapiro Condition -- 6.3 Kernel Estimates -- 6.4 Solution Operators -- 7 Elliptic Problems in a Half Space: Banach Spaces of Class HT -- 7.1 H[sup(∞)]-Calculus -- 7.2 R-Bounds for Solution Operators -- 7.3 Perturbations -- 7.4 Variable Coeffients in a Half Space -- 8 Elliptic and Parabolic Problems in Domains -- 8.1 Localization Techniques and Main Result for Domains -- 8.2 Proof of the Main Result for Domains -- Notes -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.