Pointwise Convergence of Fourier Series

  • Authors
  • Juan Arias de Reyna

Part of the Lecture Notes in Mathematics book series (LNM, volume 1785)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Juan Arias de Reyna
    Pages 3-10
  3. Juan Arias de Reyna
    Pages 11-29
  4. Juan Arias de Reyna
    Pages 31-44
  5. Juan Arias de Reyna
    Pages 47-49
  6. Juan Arias de Reyna
    Pages 51-72
  7. Juan Arias de Reyna
    Pages 73-76
  8. Juan Arias de Reyna
    Pages 77-84
  9. Juan Arias de Reyna
    Pages 85-91
  10. Juan Arias de Reyna
    Pages 93-102
  11. Juan Arias de Reyna
    Pages 103-115
  12. Juan Arias de Reyna
    Pages 117-123
  13. Juan Arias de Reyna
    Pages 127-143
  14. Juan Arias de Reyna
    Pages 145-162
  15. Juan Arias de Reyna
    Pages 163-166
  16. Juan Arias de Reyna
    Pages 167-169
  17. Juan Arias de Reyna
    Pages 171-175
  18. Back Matter
    Pages 177-179

About this book

Introduction

This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.

Keywords

Carleson theorem Fourier series calculus convergence function maximal operator proof theorem

Bibliographic information

  • DOI https://doi.org/10.1007/b83346
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43270-8
  • Online ISBN 978-3-540-45822-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book