Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

Steve Hofmann*, Guozhen Lu, Dorina Mitrea, Marius Mitrea, Lixin Yan

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    185 Citations (Scopus)

    Abstract

    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 we 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 ℝ n with a non-negative, locally integrable potential, we establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, we define Hardy spaces H L p(X) for p > 1, which may or may not coincide with the space L p(X), and show that they interpolate with H L 1(X) spaces by the complex method.

    Original languageEnglish
    Pages (from-to)1-84
    Number of pages84
    JournalMemoirs of the American Mathematical Society
    Volume214
    Issue number1007
    DOIs
    Publication statusPublished - Nov 2011

    Keywords

    • Atom
    • BMO
    • Davies-Gaffney condition
    • Hardy space
    • Molecule
    • Non-negative self-adjoint operator
    • Schrödinger operators
    • Space of homogeneous type

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