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<p>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.</p>

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Sparse Domination Via the Calderón-Zygmund Decomposition: the Example of Dini-Smooth Kernels

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月10日

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  • Fernando Ballesta-Yagüe,
  • José M. Conde-Alonso

摘要

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.