Martingales and Littlewood-Paley theory
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 evolut...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Cham
Springer International Publishing
2016
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| Schriftenreihe: | Hytönen, Tuomas Analysis in Banach spaces.
volume 1 Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, volume 63 |
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Tag hinzufügen | Zusammenfassung: | 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 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 |
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| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xvi, 614 Seiten Illustrationen, Diagramme |
| ISBN: | 9783319485195 978-3-319-48519-5 |