Weighted bounds for multilinear square functions

The Anh Bui, Mahdi Hormozi*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)

    Abstract

    Let P→ = (p1, … , pm) with 1 < p1, …, pm < ∞, 1/p1+⋯+1/pm=1/p and w→ = (w1, … , wm) ∈ AP→. In this paper, we investigate the weighted bounds with dependence on aperture α for multilinear square functions Sα,ψ(f→ ). We show that (Formula presented.). This result extends the result in the linear case which was obtained by Lerner in 2014. Our proof is based on the local mean oscillation technique presented firstly to find the weighted bounds for Calderón–Zygmund operators. This method helps us avoiding intrinsic square functions in the proof of our main result.

    Original languageEnglish
    Pages (from-to)135-148
    Number of pages14
    JournalPotential Analysis
    Volume46
    Issue number1
    Early online date2 Aug 2016
    DOIs
    Publication statusPublished - Jan 2017

    Keywords

    • Multilinear singular integrals
    • Weighted norm inequalities
    • Aperture dependence

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