# Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates

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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.