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Record Nr. |
UNINA9910155299603321 |
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Autore |
Hytönen Tuomas |
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Titolo |
Analysis in Banach Spaces : Volume I: Martingales and Littlewood-Paley Theory / / by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
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Edizione |
[1st ed. 2016.] |
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Descrizione fisica |
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1 online resource (XVII, 614 p. 3 illus.) |
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Collana |
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Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, , 0071-1136 ; ; 63 |
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Disciplina |
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Soggetti |
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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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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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 |
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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. |
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