A note on weighted bounds for singular operators with nonsmooth kernels

The Anh Bui, José M. Conde-Alonso, Xuan Thinh Duong, Mahdi Hormozi

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)

    Abstract

    Let T be a multilinear integral operator which is bounded on certain products of Lebesgue spaces on ℝn. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual Hölder continuity of kernels of multilinear Calderón-Zygmund singular integral operators. In this paper, given a suitable multiple weight w→, we obtain a bound for the weighted norm of T in terms of w→. As applications, we obtain new weighted bounds for certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schrödinger operators on ℝn.

    Original languageEnglish
    Pages (from-to)245-269
    Number of pages25
    JournalStudia Mathematica
    Volume236
    Issue number3
    DOIs
    Publication statusPublished - 2017

    Keywords

    • multilinear singular integrals
    • weighted norm inequalities
    • Lerner's formula
    • multilinear Fourier multipliers

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