Expository article examines sparse domination using Calderón-Zygmund decomposition, highlighting challenges with Dini-smooth kernels and nondoubling measures.
In this expository article, we briefly survey the main known schemes of proof of sparse domination principles within harmonic analysis. We then use the one based on the Calderón-Zygmund decomposition to prove a dual sparse domination estimate for Calderón-Zymgund operators with Dini-smooth kernels, with an eye on the difficulties that arise when trying to transfer the argument to spaces with nondoubling measures.
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Ballesta-Yagüe et al. (2025) studied this question.