04281nam 22007095 450 991015529960332120200704092935.010.1007/978-3-319-48520-1(CKB)3710000000964824(DE-He213)978-3-319-48520-1(MiAaPQ)EBC4749253(PPN)197137695(EXLCZ)99371000000096482420161128d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierAnalysis in Banach Spaces Volume I: Martingales and Littlewood-Paley Theory /by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (XVII, 614 p. 3 illus.)Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,0071-1136 ;633-319-48519-9 3-319-48520-2 Includes bibliographical references and index.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.Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,0071-1136 ;63Fourier analysisMeasure theoryPartial differential equationsProbabilitiesFunctional analysisFourier Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12058Measure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Fourier analysis.Measure theory.Partial differential equations.Probabilities.Functional analysis.Fourier Analysis.Measure and Integration.Partial Differential Equations.Probability Theory and Stochastic Processes.Functional Analysis.510Hytönen Tuomasauthttp://id.loc.gov/vocabulary/relators/aut748040van Neerven Janauthttp://id.loc.gov/vocabulary/relators/autVeraar Markauthttp://id.loc.gov/vocabulary/relators/autWeis Lutzauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910155299603321Analysis in Banach Spaces1989901UNINA