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Martingale Hardy Spaces and their Applications in Fourier Analysis

  • Authors
  • Ferenc Weisz

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

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Ferenc Weisz
    Pages 1-12
  3. Ferenc Weisz
    Pages 13-79
  4. Ferenc Weisz
    Pages 80-140
  5. Ferenc Weisz
    Pages 141-163
  6. Ferenc Weisz
    Pages 164-182
  7. Back Matter
    Pages 204-220

About this book

Introduction

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

  • DOI https://doi.org/10.1007/BFb0073448
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57623-5
  • Online ISBN 978-3-540-48295-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site