Variation of CalderónZygmund operators with matrix weight

Xuan Thinh Duong, Ji Li*, Dongyong Yang

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    Let p (1,∞), ρ (2,∞) and W be a matrix Ap weight. In this paper, we introduce a version of variation Vρ(Tn, - ∗) for matrix Calderón-Zygmund operators with modulus of continuity satisfying the Dini condition. We then obtain the Lp(W)-boundedness of Vρ(Tn, - ∗) with norm (equation presented) by first proving a sparse domination of the variation of the scalar Calderón-Zygmund operator, and then providing a convex body sparse domination of the variation of the matrix Calderón-Zygmund operator. The key step here is a weak type estimate of a local grand maximal truncated operator with respect to the scalar Calderón-Zygmund operator.

    Original languageEnglish
    Article number2050062
    Pages (from-to)2050062-1-2050062-30
    Number of pages30
    JournalCommunications in Contemporary Mathematics
    Volume23
    Issue number7
    Early online date24 Oct 2020
    DOIs
    Publication statusPublished - Nov 2021

    Keywords

    • CalderónZygmund operator
    • variation
    • matrix weight
    • sparse operator

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