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© 1977

Littlewood-Paley and Multiplier Theory

Book

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 90)

Table of contents

  1. Front Matter
    Pages i-ix
  2. R. E. Edwards, G. I. Gaudry
    Pages 1-3
  3. R. E. Edwards, G. I. Gaudry
    Pages 4-29
  4. R. E. Edwards, G. I. Gaudry
    Pages 30-49
  5. R. E. Edwards, G. I. Gaudry
    Pages 50-56
  6. R. E. Edwards, G. I. Gaudry
    Pages 57-75
  7. R. E. Edwards, G. I. Gaudry
    Pages 76-103
  8. R. E. Edwards, G. I. Gaudry
    Pages 166-176
  9. Back Matter
    Pages 177-214

About this book

Introduction

This book is intended to be a detailed and carefully written account of various versions of the Littlewood-Paley theorem and of some of its applications, together with indications of its general significance in Fourier multiplier theory. We have striven to make the presentation self-contained and unified, and adapted primarily for use by graduate students and established mathematicians who wish to begin studies in these areas: it is certainly not intended for experts in the subject. It has been our experience, and the experience of many of our students and colleagues, that this is an area poorly served by existing books. Their accounts of the subject tend to be either ill-suited to the needs of a beginner, or fragmentary, or, in one or two instances, obscure. We hope that our book will go some way towards filling this gap in the literature. Our presentation of the Littlewood-Paley theorem proceeds along two main lines, the first relating to singular integrals on locally com­ pact groups, and the second to martingales. Both classical and modern versions of the theorem are dealt with, appropriate to the classical n groups IRn, ?L , Tn and to certain classes of disconnected groups. It is for the disconnected groups of Chapters 4 and 5 that we give two separate accounts of the Littlewood-Paley theorem: the first Fourier analytic, and the second probabilistic.

Keywords

Fourier Analysis Harmonische Analyse Littlewood-Paleyscher Satz Martingales Multiplikator (Math.) differential equation theorem

Authors and affiliations

  1. 1.Institute of Advanced StudiesAustralian National UniversityCanberraAustralia
  2. 2.Flinders UniversityBedford ParkAustralia

Bibliographic information

  • Book Title Littlewood-Paley and Multiplier Theory
  • Authors R. E. Edwards
    G. I. Gaudry
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete
  • DOI https://doi.org/10.1007/978-3-642-66366-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1977
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-07726-8
  • Softcover ISBN 978-3-642-66368-0
  • eBook ISBN 978-3-642-66366-6
  • Series ISSN 0071-1136
  • Edition Number 1
  • Number of Pages X, 214
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site