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<p>We prove sharp local and global variation bounds for the centred Hardy–Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both the continuous and discrete settings and extend our results to a larger class of functions.</p>

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The One-Dimensional Centred Maximal Function Diminishes the Variation of Indicator Functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月7日

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  • Constantin Bilz,
  • Julian Weigt

摘要

We prove sharp local and global variation bounds for the centred Hardy–Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both the continuous and discrete settings and extend our results to a larger class of functions.