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Martingale Hardy Spaces and their Applications in Fourier Analysis

  • Book
  • © 1994

Overview

Authors:
  1. Ferenc Weisz
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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
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  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. Inequalities for Vilenkin-fourier coefficients

    • Ferenc Weisz
    Pages 183-203

  8. Back Matter

    Pages 204-220
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Keywords

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.

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 and Stochastic Processes, Analysis

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