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Hardy Spaces on the Euclidean Space

  • Authors
  • Akihito Uchiyama

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Akihito Uchiyama
    Pages 1-11
  3. Akihito Uchiyama
    Pages 13-28
  4. Akihito Uchiyama
    Pages 29-37
  5. Akihito Uchiyama
    Pages 39-50
  6. Akihito Uchiyama
    Pages 61-69
  7. Akihito Uchiyama
    Pages 111-120
  8. Akihito Uchiyama
    Pages 129-133
  9. Akihito Uchiyama
    Pages 135-144
  10. Akihito Uchiyama
    Pages 145-160
  11. Akihito Uchiyama
    Pages 161-165
  12. Akihito Uchiyama
    Pages 187-189
  13. Akihito Uchiyama
    Pages 191-199
  14. Akihito Uchiyama
    Pages 223-227
  15. Akihito Uchiyama
    Pages 285-288
  16. Back Matter
    Pages 293-305

About this book

Introduction

"Still waters run deep." This proverb expresses exactly how a mathematician Akihito Uchiyama and his works were. He was not celebrated except in the field of harmonic analysis, and indeed he never wanted that. He suddenly passed away in summer of 1997 at the age of 48. However, nowadays his contributions to the fields of harmonic analysis and real analysis are permeating through various fields of analysis deep and wide. One could write several papers explaining his contributions and how they have been absorbed into these fields, developed, and used in further breakthroughs. Peter W. Jones (Professor of Yale University) says in his special contribution to this book that Uchiyama's decomposition of BMO functions is considered to be the Mount Everest of Hardy space theory. This book is based on the draft, which the author Akihito Uchiyama had completed by 1990. It deals with the theory of real Hardy spaces on the n-dimensional Euclidean space. Here the author explains scrupulously some of important results on Hardy spaces by real-variable methods, in particular, the atomic decomposition of elements in Hardy spaces and his constructive proof of the Fefferman-Stein decomposition of BMO functions into the sum of a bounded?function and Riesz transforms of bounded functions.

Keywords

Dimension Hardy Spaces bounded mean oscillation maximum subharmonic function

Bibliographic information

  • DOI https://doi.org/10.1007/978-4-431-67905-9
  • Copyright Information Springer-Verlag Tokyo 2001
  • Publisher Name Springer, Tokyo
  • eBook Packages Springer Book Archive
  • Print ISBN 978-4-431-67999-8
  • Online ISBN 978-4-431-67905-9
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site
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