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  • © 2002

Pointwise Convergence of Fourier Series

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

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XIV
  2. 1. Hardy-Littlewood maximal function

    • Juan Arias de Reyna
    Pages 3-10
  3. 2. Fourier Series

    • Juan Arias de Reyna
    Pages 11-29
  4. 3. Hilbert Transform

    • Juan Arias de Reyna
    Pages 31-44
  5. The Charleson-Hunt Theorem

    • Juan Arias de Reyna
    Pages 47-49
  6. 4. The Basic Step

    • Juan Arias de Reyna
    Pages 51-72
  7. 5. Maximal Inequalities

    • Juan Arias de Reyna
    Pages 73-76
  8. 6. Growth of Partial Sums

    • Juan Arias de Reyna
    Pages 77-84
  9. 7. Carleson analysis of the function

    • Juan Arias de Reyna
    Pages 85-91
  10. 8. Allowed Pairs

    • Juan Arias de Reyna
    Pages 93-102
  11. 9. Pair Interchange Theorems

    • Juan Arias de Reyna
    Pages 103-115
  12. 10. All together

    • Juan Arias de Reyna
    Pages 117-123
  13. 11. Spaces of functions

    • Juan Arias de Reyna
    Pages 127-143
  14. 12. The Maximal Operator of Fourier series

    • Juan Arias de Reyna
    Pages 145-162
  15. 13. Fourier Transform on the line

    • Juan Arias de Reyna
    Pages 163-166
  16. References

    • Juan Arias de Reyna
    Pages 167-169
  17. Comments and Subject Index

    • Juan Arias de Reyna
    Pages 171-175
  18. Back Matter

    Pages 177-179

About this book

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

  • Book Title: Pointwise Convergence of Fourier Series

  • Authors: Juan Arias de Reyna

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b83346

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-43270-8

  • eBook ISBN: 978-3-540-45822-7

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVIII, 179

  • Topics: Fourier Analysis

Buying options

eBook USD 34.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-45822-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 49.95
Price excludes VAT (USA)