Weighted norm inequalities for multilinear operators and applications to multilinear Fourier multipliers

The Anh Bui*, Xuan Thinh Duong

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    30 Citations (Scopus)

    Abstract

    Let T be a multilinear operator which is bounded on certain products of unweighted Lebesgue spaces of Rn. We assume that the associated kernel of T satisfies some mild regularity condition which is weaker than the usual Hölder continuity of those in the class of multilinear Calderón-Zygmund singular integral operators. We then show the boundedness for T and the boundedness of the commutator of T with BMO functions on products of weighted Lebesgue spaces of Rn. As an application, we obtain the weighted norm inequalities of multilinear Fourier multipliers and of their commutators with BMO functions on the products of weighted Lebesgue spaces when the number of derivatives of the symbols is the same as the best known result for the multilinear Fourier multipliers to be bounded on the products of unweighted Lebesgue spaces.

    Original languageEnglish
    Pages (from-to)63-75
    Number of pages13
    JournalBulletin des Sciences Mathematiques
    Volume137
    Issue number1
    DOIs
    Publication statusPublished - Jan 2013

    Fingerprint Dive into the research topics of 'Weighted norm inequalities for multilinear operators and applications to multilinear Fourier multipliers'. Together they form a unique fingerprint.

    Cite this