Quantitative weighted estimates for some singular integrals related to critical functions

The Anh Bui*, The Quan Bui, Xuan Thinh Duong

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    Let (X, d, μ) be a space of homogeneous type with a metric d and a doubling measure μ. Assume that ρ is a critical function on X which has an associated class of weights containing the Muckenhoupt weights as a proper subset. In this paper, we prove the quantitative weighted estimates for certain singular integrals corresponding to the new class of weights. It is important to note that the assumptions on the kernels of these singular integrals do not have any regularity conditions. Our applications include the spectral multipliers and the Riesz transforms associated to Schrödinger operators in various settings, ranging from the magnetic Schrödinger operators in Euclidean spaces to the Laguerre operators.

    Original languageEnglish
    Pages (from-to)10215-10245
    Number of pages31
    JournalJournal of Geometric Analysis
    Issue number10
    Early online date16 Mar 2021
    Publication statusPublished - Oct 2021


    • Critical function
    • Quantitative weighted estimate
    • Sparse operator


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