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  • © 1994

Martingale Hardy Spaces and their Applications in Fourier Analysis

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1568)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VIII
  2. Preliminaries and notations

    • Ferenc Weisz
    Pages 1-12
  3. One-parameter Martingale Hardy spaces

    • Ferenc Weisz
    Pages 13-79
  4. Two-Parameter Martingale Hardy spaces

    • Ferenc Weisz
    Pages 80-140
  5. Tree martingales

    • Ferenc Weisz
    Pages 141-163
  6. Real interpolation

    • Ferenc Weisz
    Pages 164-182
  7. Back Matter

    Pages 204-220

About this book

This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.

Keywords

  • Fourier series
  • Fourier-Analysis
  • Hardy and BMO spaces
  • Hardy's inequality
  • Martingale
  • Martingales
  • One- and two-parameter martingales
  • Probability theory
  • Propability
  • Walsh- and Vilenkin-series
  • calculus
  • tree martingales

Bibliographic Information

  • Book Title: Martingale Hardy Spaces and their Applications in Fourier Analysis

  • Authors: Ferenc Weisz

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0073448

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-57623-5Published: 28 March 1994

  • eBook ISBN: 978-3-540-48295-6Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 224

  • Topics: Probability Theory, Analysis

Buying options

eBook USD 44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions