Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates
Author(s)
Bibliographic Information
Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates
（Memoirs of the American Mathematical Society, no. 1007）
American Mathematical Society, c2011
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"November 2011, volume 214, number 1007 (third of 5 numbers)."
Includes bibliography (p. 75-78)
Other authors: Guozhen Lu, Dorina Mitrea, Marius Mitrea, Lixin Yan
Description and Table of Contents
Description
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 Schrodinger 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.
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