Analysis in Banach Spaces

Volume II: Probabilistic Methods and Operator Theory

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

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 1-52
  3. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 53-162
  4. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 163-250
  5. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 251-358
  6. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 359-478
  7. Back Matter
    Pages 479-616

About this book

Introduction

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations. 



Keywords

46Bxx, 35Kxx, 47Axx, 60Hxx, 42Bxx R-boundedness Square Function Estimates Radonifying operators probability in Banach spaces H∞ functional calculus

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-69808-3
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-69807-6
  • Online ISBN 978-3-319-69808-3
  • Series Print ISSN 0071-1136
  • Series Online ISSN 2197-5655
  • About this book