On multilinear Littlewood-Paley operators

Xi Chen, Qingying Xue*, Kôzô Yabuta

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    21 Citations (Scopus)

    Abstract

    In this paper, we established the weighted estimates for the multilinear Littlewood-Paley operators, including the multilinear Marcinkiewicz integral and the multilinear area integral of Lusin. These operators are generalizations of the linear operators for higher dimension which were first defined and studied by E.M. Stein in 1958. Strong Lp11)×⋯×Lpm(ωm)→Lp(νω→) estimates when each pi>1 and weak type Lp1(ω1)×⋯×Lpm(ωm)→Lp,(νω→) estimates if there is a pi=1 are obtained, where νω→=i=1mωippi and each wi(i=1,...,m) is a nonnegative function on Rn.

    Original languageEnglish
    Pages (from-to)25-40
    Number of pages16
    JournalNonlinear Analysis, Theory, Methods and Applications
    Volume115
    DOIs
    Publication statusPublished - Feb 2015

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