Analysis in Banach Spaces : Volume I: Martingales and Littlewood-Paley Theory. 1st ed. 2016

種類:

電子ブック

責任表示:

by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2016

著者名:

• Hytönen, Tuomas.
• van Neerven, Jan.
• Veraar, Mark.
• Weis, Lutz.
• SpringerLink (Online service)

シリーズ名:

Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ; 63

ISBN:

9783319485201 [3319485202]    

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 a

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