Analysis in Banach Spaces [electronic resource] : Volume I: Martingales and Littlewood-Paley Theory / by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis.

Hytönen, Tuomas [Browse]
1st ed. 2016.
Cham : Springer International Publishing : Imprint: Springer, 2016.
1 online resource (XVII, 614 p. 3 illus.)


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Summary note
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.
Bibliographic references
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.
  • 10.1007/978-3-319-48520-1
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