Advertisement

Analysis in Banach Spaces

Volume I: Martingales and Littlewood-Paley Theory

  • Tuomas Hytönen
  • Jan van Neerven
  • Mark Veraar
  • Lutz Weis
Book

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 1-66
  3. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 67-164
  4. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 165-266
  5. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 267-372
  6. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 373-492
  7. Back Matter
    Pages 493-614

About this book

Introduction

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.

Keywords

46Bxx, 42Bxx, 60Gxx UMD Spaces Bochner integration Conditional Expectations Hilbert transform Fourier multipliers

Authors and affiliations

  • Tuomas Hytönen
    • 1
  • Jan van Neerven
    • 2
  • Mark Veraar
    • 3
  • Lutz Weis
    • 4
  1. 1.Dep Mathematics & StatisticsUniversity of Helsinki Dep Mathematics & StatisticsHelsinkiFinland
  2. 2.EEMCS/DIAMTU Delft DelftThe Netherlands
  3. 3.Delft University of Technology DelftThe Netherlands
  4. 4.Karlsruhe Institute of Technology KarlsruheGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-48520-1
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-48519-5
  • Online ISBN 978-3-319-48520-1
  • Series Print ISSN 0071-1136
  • Series Online ISSN 2197-5655
  • Buy this book on publisher's site