Sharp weighted estimates for square functions associated to operators on spaces of homogeneous type

The Anh Bui*, Xuan Thinh Duong

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)

    Abstract

    Let X be a metric space with a doubling measure and let L be a linear operator in L2 (X) which generates a semigroup e -tL whose kernels pt(x, y) , t > 0 , satisfy the Gaussian upper bound. In this article, we prove sharp L wp norm inequalities for a number of square functions associated to L including the vertical square functions, the Lusin area integral square functions and the Littlewood–Paley g-functions. We note that our conditions on the heat kernels pt (x, y) are mild in the sense that the associated kernels of the square functions do not possess enough regularity for those operators to belong to the standard class of Calderón–Zygmund operators.

    Original languageEnglish
    Pages (from-to)874-900
    Number of pages27
    JournalJournal of Geometric Analysis
    Volume30
    Issue number1
    Early online date4 Mar 2019
    DOIs
    Publication statusPublished - Jan 2020

    Keywords

    • Heat kernel
    • Square function
    • Sharp weighted estimate

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