Memoirs of the American Mathematical Society 2011; 78 pp; softcover Volume: 214 ISBN10: 0821852388 ISBN13: 9780821852385 List Price: US$66 Individual Members: US$39.60 Institutional Members: US$52.80 Order Code: MEMO/214/1007
 Let \(X\) be a metric space with doubling measure, and \(L\) be a nonnegative, selfadjoint operator satisfying DaviesGaffney 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 nonnegative, 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  Introduction
 Notation and preliminaries
 DaviesGaffney estimates
 The decomposition into atoms
 Relations between atoms and molecules
 \(\mathrm{BMO}_{L,M}(X)\): Duality with Hardy spaces
 Hardy spaces and Gaussian estimates
 Hardy spaces associated to Schrödinger operators
 Further properties of Hardy spaces associated to operators
 Bibliography
