Cover Image

Hardy Spaces on the Euclidean Space /

"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 hi...

Full description

Bibliographic Details
Main Author: Uchiyama, Akihito
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Tokyo : Springer Japan, 2001.
Series:Springer monographs in mathematics.
Subjects:
Mathematics.
Geometry, Algebraic.
Number theory.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Foreword
  • Recollections of My Good Friend, Akihito Uchiyama by Peter W. Jones
  • Preface
  • Introduction
  • Lipschitz spaces and BMO
  • Atomic Hp sapces
  • Atomic decomposition from grand maximal functions
  • Atomic decomposition from S functions
  • Hardy-Littlewood-Fefferman-Stein type inequalities, 1
  • Hardy-Littlewood-Fefferman-Stein type inequalities, 2
  • Hardy-Littlewood-Fefferman-Stein type inequalities, 3
  • Grand maximal function from radial maximal functions
  • S-functions from g-functions Good lambda inequalities for nontangential maximal functions and S-functions of harmonic functions
  • A direct proof (special characters)
  • A direct proof of (special characters)
  • Subharmonicity 1
  • Subharmonicity 2
  • Preliminaries for characterizations of H in terms of Fourier multipliers
  • Characterization of Hp in terms of Riesz transforms
  • Other results on the characterization of Hp in terms of Fourier multipliers
  • Fefferman's original proof of (special characters)
  • Varopoulos's proof of the above inequality
  • The Fefferman-Stein decomposition of BMO
  • A constructive proof of the Fefferman-Stein decomposition of BMO
  • Vector-valued unimodular BMO functions
  • Extensions of the Fefferman-Stein decomposition of BMO, 1
  • Characterization of H1 in terms of Fourier multipliers
  • Extension of the Fefferman-Stein decomposition of BMO, 2
  • Characterization of Hp in terms of Fourier multipliers
  • The one-dimensional case
  • Appendix
  • References
  • Index.