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Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates
Steve Hofmann, University of Missouri-Columbia, MO, Guozhen Lu, Wayne State University, Detroit, MI, Dorina Mitrea and Marius Mitrea, University of Missouri-Columbia, MO, and Lixin Yan, Zhongshan University, Guangzhou, People's Republic of China
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Memoirs of the American Mathematical Society
2011; 78 pp; softcover
Volume: 214
ISBN-10: 0-8218-5238-8
ISBN-13: 978-0-8218-5238-5
List Price: US$70 Individual Members: US$42
Institutional Members: US\$56
Order Code: MEMO/214/1007

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.

• $$\mathrm{BMO}_{L,M}(X)$$: Duality with Hardy spaces