Commutators of multiparameter flag singular integrals and applications

Xuan Thinh Duong, Ji Li, Yumeng Ou, Jill Pipher, Brett D. Wick

    Research output: Contribution to journalArticlepeer-review

    12 Citations (Scopus)


    We introduce the iterated commutator for the Riesz transforms in the multiparameter flag setting, and prove the upper bound of this commutator with respect to the symbol b in the flag BMO space. Our methods require the techniques of semigroups, harmonic functions and multiparameter flag Littlewood-Paley analysis. We also introduce the big commutator in this multiparameter flag setting and prove the upper bound with symbol b in the flag little bmo space by establishing the "exponential-logarithmic" bridge between this flag little bmo space and the Muckenhoupt Ap weights with flag structure. As an application, we establish the div-curl lemmas with respect to the appropriate Hardy spaces in the multiparameter flag setting.

    Original languageEnglish
    Pages (from-to)1325-1355
    Number of pages31
    JournalAnalysis and PDE
    Issue number5
    Publication statusPublished - 1 Jan 2019


    • BMO space
    • Div-curl lemma
    • Flag commutator
    • Hardy space
    • Multiparameter flag setting


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