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 journalArticle


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
Issue number1
Early online date4 Mar 2019
Publication statusPublished - Jan 2020



  • Heat kernel
  • Square function
  • Sharp weighted estimate

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