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Group theory --- Operator theory --- 517.986 --- 51 --- Topological algebras. Theory of infinite-dimensional representations --- Mathematics --- 51 Mathematics --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Linear operators --- Semigroups of operators. --- Linear operators.

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This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations. .

Banach spaces. --- Probabilities. --- Operator theory. --- Mathematics. --- Fourier analysis. --- Functional analysis. --- Partial differential equations. --- Functional Analysis. --- Operator Theory. --- Fourier Analysis. --- Partial Differential Equations. --- Probability Theory and Stochastic Processes. --- Functional analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Functions of complex variables --- Generalized spaces --- Topology --- Differential equations, partial. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Partial differential equations --- Analysis, Fourier --- Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

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The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.

Functional analysis --- Harmonic analysis. Fourier analysis --- Partial differential equations --- Operational research. Game theory --- Probability theory --- Mathematics --- Measuring methods in physics --- Mathematical physics --- Fourieranalyse --- differentiaalvergelijkingen --- waarschijnlijkheidstheorie --- stochastische analyse --- functies (wiskunde) --- meettechniek --- wiskunde --- kansrekening

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The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes.  The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.

Fourier analysis. --- Measure theory. --- Partial differential equations. --- Probabilities. --- Functional analysis. --- Fourier Analysis. --- Measure and Integration. --- Partial Differential Equations. --- Probability Theory and Stochastic Processes. --- Functional Analysis.

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This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Functional analysis. --- Fourier analysis. --- Harmonic analysis. --- Operator theory. --- Mathematical analysis. --- Functional Analysis. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Operator Theory. --- Analysis.