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Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates
 
Steve Hofmann University of Missouri-Columbia, Columbia, MO
Guozhen Lu Wayne State University, Detroit, MI
Dorina Mitrea University of Missouri-Columbia, Columbia, MO
Marius Mitrea University of Missouri-Columbia, Columbia, MO
Lixin Yan Zhongshan University, Guangzhou, People’s Republic of China
Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates
eBook ISBN:  978-1-4704-0624-0
Product Code:  MEMO/214/1007.E
List Price: $70.00
MAA Member Price: $63.00
AMS Member Price: $42.00
Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates
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Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates
Steve Hofmann University of Missouri-Columbia, Columbia, MO
Guozhen Lu Wayne State University, Detroit, MI
Dorina Mitrea University of Missouri-Columbia, Columbia, MO
Marius Mitrea University of Missouri-Columbia, Columbia, MO
Lixin Yan Zhongshan University, Guangzhou, People’s Republic of China
eBook ISBN:  978-1-4704-0624-0
Product Code:  MEMO/214/1007.E
List Price: $70.00
MAA Member Price: $63.00
AMS Member Price: $42.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2142011; 78 pp
    MSC: Primary 42; Secondary 46; 47;

    Let \(X\) be a metric space with doubling measure, and \(L\) be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on \(L^2(X)\). In this article the authors present a theory of Hardy and BMO spaces associated to \(L\), including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Further specializing to the case that \(L\) is a Schrödinger operator on \(\mathbb{R}^n\) with a non-negative, locally integrable potential, the authors establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, they define Hardy spaces \(H^p_L(X)\) for \(p>1\), which may or may not coincide with the space \(L^p(X)\), and show that they interpolate with \(H^1_L(X)\) spaces by the complex method.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Notation and preliminaries
    • 3. Davies-Gaffney estimates
    • 4. The decomposition into atoms
    • 5. Relations between atoms and molecules
    • 6. ${\rm BMO}_{L,M}(X)$: Duality with Hardy spaces
    • 7. Hardy spaces and Gaussian estimates
    • 8. Hardy spaces associated to Schrödinger operators
    • 9. Further properties of Hardy spaces associated to operators
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2142011; 78 pp
MSC: Primary 42; Secondary 46; 47;

Let \(X\) be a metric space with doubling measure, and \(L\) be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on \(L^2(X)\). In this article the authors present a theory of Hardy and BMO spaces associated to \(L\), including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Further specializing to the case that \(L\) is a Schrödinger operator on \(\mathbb{R}^n\) with a non-negative, locally integrable potential, the authors establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, they define Hardy spaces \(H^p_L(X)\) for \(p>1\), which may or may not coincide with the space \(L^p(X)\), and show that they interpolate with \(H^1_L(X)\) spaces by the complex method.

  • Chapters
  • 1. Introduction
  • 2. Notation and preliminaries
  • 3. Davies-Gaffney estimates
  • 4. The decomposition into atoms
  • 5. Relations between atoms and molecules
  • 6. ${\rm BMO}_{L,M}(X)$: Duality with Hardy spaces
  • 7. Hardy spaces and Gaussian estimates
  • 8. Hardy spaces associated to Schrödinger operators
  • 9. Further properties of Hardy spaces associated to operators
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.