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© 2017

Analysis in Banach Spaces

Volume II: Probabilistic Methods and Operator Theory

  • Offers the first comprehensive treatment of R-boundedness, Banach space-valued square functions and ?-radonifying operators

  • Develops their deep connections with the holomorphic functional calculus of sectorial and bi-sectorial operators

  • Offers a self-contained presentation and complete, detailed proofs of results in both the core and the background material

Book

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

  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

About the authors

Tuomas Hytönen is Professor at the University of Helsinki. A leading expert in Harmonic Analysis with over 60 research papers, he was educated at Helsinki University of Technology and spent a postdoc year at Delft University of Technology. He received a European Research Council Starting Grant in 2011 and gave an invited address to the International Congress of Mathematicians in 2014.

Jan van Neerven is Professor of Analysis at Delft University of Technology. Author of more than 100 research papers and two monographs, he is a leading expert in Operator Theory and Stochastic Analysis. He held post-doctoral positions at Caltech and Tübingen University. He was awarded a Human Capital and Mobility fellowship, a fellowship of the Royal Dutch Academy of Arts and Sciences, and VIDI and VICI subsidies from the Netherlands Organisation for Scientific Research.

Mark Veraar is Associate Professor at Delft University of Technology. Author of over 40 research papers, he is a leading researcher in the theory of evolution equations and stochastic partial differential equations. He held post-doctoral positions at the Universities of Warsaw and Karlsruhe, the latter with a Alexander von Humboldt Fellowship. He is the recipient of VENI and VIDI grants from the Netherlands Organisation for Scientific Research.

Lutz Weis, a Professor at Karlsruhe Institute of Technology, is a senior researcher in operator theory and evolution equations. He has published over 80 research papers and a monograph. Since receiving his PhD from University of Bonn, he was a professor at Louisiana State University and visiting professor at TU Berlin as well as Universities of Kiel, South Carolina and Minnesota. He organized a Marie Curie training site and is currently a member of a DFG Graduiertenkolleg.

Bibliographic information

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Reviews

“The book will become an invaluable reference for graduate students and researchers. Those interested in functional analysis, harmonic analysis and stochastic analysis will appreciate the detailed treatment of the theory of R-boundedness, radonifying operators and holomorphic functional calculus developed over the last 20 years.” (Oscar Blasco, zbMATH 1402.46002, 2019)