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＜電子ブック＞
Analysis in Banach Spaces : Volume I: Martingales and Littlewood-Paley Theory / by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 63)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
本文言語	英語
大きさ	XVII, 614 p. 3 illus : online resource
著者標目	*Hytönen, Tuomas author van Neerven, Jan author Veraar, Mark author Weis, Lutz author SpringerLink (Online service)
件　名	LCSH:Fourier analysis LCSH:Measure theory LCSH:Differential equations LCSH:Probabilities LCSH:Functional analysis FREE:Fourier Analysis FREE:Measure and Integration FREE:Differential Equations FREE:Probability Theory FREE:Functional Analysis
一般注記	1.Bochner Spaces -- 2.Operators on Bochner Spaces -- 3.Martingales -- 4.UMD spaces -- 5. Hilbert transform and Littlewood-Paley Theory -- 6.Open Problems -- A.Mesaure Theory -- B.Banach Spaces -- C.Interpolation Theory -- D.Schatten classes 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 HTTP:URL=https://doi.org/10.1007/978-3-319-48520-1

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