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Hardy Spaces on the Euclidean Space

  • Book
  • © 2001

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Authors:
  1. Akihito Uchiyama
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Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (29 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Introduction

    • Akihito Uchiyama
    Pages 1-11

  3. Lipschitz spaces and BMO

    • Akihito Uchiyama
    Pages 13-28

  4. Atomic H p spaces

    • Akihito Uchiyama
    Pages 29-37

  5. Operators on H p

    • Akihito Uchiyama
    Pages 39-50

  6. Atomic decomposition from grand maximal functions

    • Akihito Uchiyama
    Pages 51-59

  7. Atomic decomposition from S-functions

    • Akihito Uchiyama
    Pages 61-69

  8. Hardy-Littlewood-Fefferman-Stein type inequalities, 1

    • Akihito Uchiyama
    Pages 71-81

  9. Hardy-Littlewood-Fefferman-Stein type inequalities, 2

    • Akihito Uchiyama
    Pages 83-99

  10. Hardy-Littlewood-Fefferman-Stein type inequalities, 3

    • Akihito Uchiyama
    Pages 101-107

  11. Grand maximal functions from radial maximal functions

    • Akihito Uchiyama
    Pages 109-110

  12. S-functions from g-functions

    • Akihito Uchiyama
    Pages 111-120

  13. Good λ inequalities for nontangential maximal functions and S-functions of harmonic functions

    • Akihito Uchiyama
    Pages 121-128

  14. A direct proof of

    • Akihito Uchiyama
    Pages 129-133

  15. A direct proof of

    • Akihito Uchiyama
    Pages 135-144

  16. Subharmonicity, 1

    • Akihito Uchiyama
    Pages 145-160

  17. Subharmonicity, 2

    • Akihito Uchiyama
    Pages 161-165

  18. Preliminaries for characterizations of H p in terms of Fourier multipliers

    • Akihito Uchiyama
    Pages 167-172

  19. Characrterization of H p in terms of Riesz transforms

    • Akihito Uchiyama
    Pages 173-176

  20. Other results on the characterization of H p in terms of Fourier multipliers

    • Akihito Uchiyama
    Pages 177-182
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Keywords

About this book

"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.

Bibliographic Information

  • Book Title: Hardy Spaces on the Euclidean Space

  • Authors: Akihito Uchiyama

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-4-431-67905-9

  • Publisher: Springer Tokyo

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Japan 2001

  • Hardcover ISBN: 978-4-431-70319-8Published: 01 July 2001

  • Softcover ISBN: 978-4-431-67999-8Published: 03 October 2013

  • eBook ISBN: 978-4-431-67905-9Published: 06 December 2012

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XIII, 305

  • Topics: Number Theory, Algebraic Geometry

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