Commutators of multiparameter flag singular integrals and applications

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

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    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.

    LanguageEnglish
    Pages1325-1355
    Number of pages31
    JournalAnalysis and PDE
    Volume12
    Issue number5
    DOIs
    Publication statusPublished - 1 Jan 2019

    Fingerprint

    Electric commutators
    Singular Integrals
    Commutator
    Ap Weights
    Muckenhoupt Weights
    BMO Space
    Upper bound
    Harmonic functions
    Riesz Transform
    Curl
    Hardy Space
    Harmonic Functions
    Lemma
    Logarithmic
    Semigroup

    Cite this

    Duong, Xuan Thinh ; Li, Ji ; Ou, Yumeng ; Pipher, Jill ; Wick, Brett D. / Commutators of multiparameter flag singular integrals and applications. In: Analysis and PDE. 2019 ; Vol. 12, No. 5. pp. 1325-1355.
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    Commutators of multiparameter flag singular integrals and applications. / Duong, Xuan Thinh; Li, Ji; Ou, Yumeng; Pipher, Jill; Wick, Brett D.

    In: Analysis and PDE, Vol. 12, No. 5, 01.01.2019, p. 1325-1355.

    Research output: Contribution to journalArticleResearchpeer-review

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    AU - Duong,Xuan Thinh

    AU - Li,Ji

    AU - Ou,Yumeng

    AU - Pipher,Jill

    AU - Wick,Brett D.

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    AB - 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.

    KW - BMO space

    KW - Div-curl lemma

    KW - Flag commutator

    KW - Hardy space

    KW - Multiparameter flag setting

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