Musielak-Orlicz Hardy spaces associated to operators satisfying Davies-Gaffney estimates and bounded holomorphic functional calculus

Xuan Thinh Duong, Tri Dung Tran

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    Let X be a metric space with doubling measure and L be an operator which satisfies Davies-Gaffney heat kernel estimates and has a bounded H1 functional calculus on L2(X). In this paper, we develop a theory of Musielak-Orlicz Hardy spaces associated to L, including a molecular decomposition, square function characterization and duality of Musielak-Orlicz Hardy spaces HL(X). Finally, we show that L has a bounded holomorphic functional calculus on HL(X) and the Riesz transform is bounded from HL(X) to L1(w).

    Original languageEnglish
    Pages (from-to)1-30
    Number of pages30
    JournalJournal of the Mathematical Society of Japan
    Volume68
    Issue number1
    DOIs
    Publication statusPublished - 2016

    Keywords

    • Musielak-Orlicz function
    • Musielak-Orlicz Hardy space
    • Functional calculus
    • Davies-Gaffney estimate
    • Riesz transform

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