The Hardy Space H1 with Non-doubling Measures and Their Applications

  • Dachun Yang
  • Dongyong Yang
  • Guoen Hu

Part of the Lecture Notes in Mathematics book series (LNM, volume 2084)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. ℝ D with Non-doubling Measures μ

    1. Front Matter
      Pages 1-3
    2. Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 5-22
    3. Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 23-58
    4. Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 59-136
    5. Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 137-214
    6. Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 215-328
  3. Non-homogeneous Spaces (X, v)

    1. Front Matter
      Pages 413-415
    2. Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 483-642
  4. Back Matter
    Pages 643-656

About this book


The present book offers an essential but accessible introduction to the discoveries first made in the 1990s that the doubling condition is superfluous for most results for function spaces and the boundedness of operators. It shows the methods behind these discoveries, their consequences and some of their applications. It also provides detailed and comprehensive arguments, many typical and easy-to-follow examples, and interesting unsolved problems.
The theory of the Hardy space is a fundamental tool for Fourier analysis, with applications for and connections to complex analysis, partial differential equations, functional analysis and geometrical analysis. It also extends to settings where the doubling condition of the underlying measures may fail.


Calderόn-Zygmund operator Hardy space Littlewood-Paley operator Non-doubling measure Non-homogeneous space

Authors and affiliations

  • Dachun Yang
    • 1
  • Dongyong Yang
    • 2
  • Guoen Hu
    • 3
  1. 1.Beijing Normal University School of Mathematical SciencesBeijingPeople's Republic of China
  2. 2.Xiamen UniversityXiamenPeople's Republic of China
  3. 3.Zhengzhou Information ScienceZhengzhouPeople's Republic of China

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2013
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-00824-0
  • Online ISBN 978-3-319-00825-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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