Sharp weighted norm inequalities for singular integrals with non–smooth kernels

The Anh Bui, Xuan Thinh Duong*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    Abstract

    In this paper, we prove the sharp weighted bound for certain singular integrals which have non-smooth kernels and do not belong to the class of standard Calderón–Zygmund operators. Our assumptions are weaker than those known in literature, since in particular we do not assume the Cotlar type inequality condition. Applications include sharp weighted estimates for the Riesz transforms associated to the Dirichlet Laplacians on open connected domains, the Riesz transforms associated to the Schrödinger operators with real potentials on the Euclidean spaces, the Riesz transforms associated to the degenerate Schrödinger operators and the Riesz transforms associated to the Schrödinger operators with inverse square potentials.

    Original languageEnglish
    Pages (from-to)1733-1750
    Number of pages18
    JournalMathematische Zeitschrift
    Volume295
    Issue number3-4
    Early online date7 Nov 2019
    DOIs
    Publication statusPublished - Aug 2020

    Keywords

    • Heat kernels
    • Singular operators
    • Weighted estimates

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