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

    9 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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