Hardy spaces associated to critical functions and applications to T1 theorems

The Anh Bui*, Xuan Thinh Duong, Luong Dang Ky

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)

    Abstract

    Let X be a metric space equipped with a measure satisfying the doubling and reverse doubling conditions. In this paper, we develop the theory of new localized Hardy spaces Hρp(X) for n/n+1<p≤1 associated to critical functions ρ defined on X where n is the doubling order. Our results include the atomic decomposition characterization and the maximal function characterization associated to an approximation of the identity. We then study the T1 criteria for singular integrals to be bounded on our Hardy spaces.

    Original languageEnglish
    Article number27
    Pages (from-to)1-67
    Number of pages67
    JournalJournal of Fourier Analysis and Applications
    Volume26
    Issue number2
    DOIs
    Publication statusPublished - Apr 2020

    Keywords

    • Hardy space
    • BMO space
    • T1 criterion
    • Schrödinger operators

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