Analysis in Banach Spaces: Volume I: Martingales and Littlewood-Paley Theory

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

Research output: Book/ReportBookScientificpeer-review

16 Citations (Scopus)


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.
Original languageEnglish
Place of PublicationCham
Number of pages492
ISBN (Electronic)978-3-319-48520-1
ISBN (Print)978-3-319-48519-5
Publication statusPublished - 2016

Publication series

NameErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
PublisherSpringer International Publishing
ISSN (Print)0071-1136


  • Fourier Analysis
  • Measure and Integration
  • Partial Differential Equations
  • Peobability Theory and Stochastic Processes
  • Functional Analysis

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