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  • © 2013

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

  • The arguments for the main results are detailed and self-contained

  • At least one typical and easily explicable example is given for each important notion further clarifying the relationship between the known and the present notions

  • Detailed references for the content of each chapter are given. Also, well-known related results and some unsolved problems, which will be of interest to the reader, are presented, which might be interesting to the reader

  • Includes supplementary material: sn.pub/extras

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

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Table of contents (8 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-3
  3. ℝ D with Non-doubling Measures μ

    1. Preliminaries

      • Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 5-22
    2. Approximations of the Identity

      • Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 23-58
    3. The Hardy Space H 1(μ)

      • Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 59-136
    4. The Local Atomic Hardy Space h 1(μ)

      • Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 137-214
    5. Boundedness of Operators over \(({\mathbb{R}}^{D},\mu )\)

      • Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 215-328
  4. Non-homogeneous Spaces (X, v)

    1. Front Matter

      Pages 413-415
    2. Boundedness of Operators over \((\mathcal{X},\nu )\)

      • Dachun Yang, Dongyong Yang, Guoen Hu
      Pages 483-642
  5. 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.

Keywords

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

Authors and Affiliations

  • Beijing Normal University School of Mathematical Sciences, Beijing, People's Republic of China

    Dachun Yang

  • Xiamen University, Xiamen, People's Republic of China

    Dongyong Yang

  • Zhengzhou Information Science, Zhengzhou, People's Republic of China

    Guoen Hu

Bibliographic Information

Buying options

eBook USD 79.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 99.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions