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<p>This work discusses self-improving properties of the Muckenhoupt condition and weighted norm inequalities for the Hardy–Littlewood maximal function on metric measure spaces with a doubling measure. Our main result provides direct proofs of these properties by applying a Whitney covering argument and a technique inspired by the Calderón–Zygmund decomposition. In particular, this approach does not rely on reverse Hölder inequalities.</p>

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Self-improving properties of weighted norm inequalities on metric measure spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月15日

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  • Juha Kinnunen,
  • Juha Lehrbäck,
  • Antti V. Vähäkangas,
  • Dachun Yang

摘要

This work discusses self-improving properties of the Muckenhoupt condition and weighted norm inequalities for the Hardy–Littlewood maximal function on metric measure spaces with a doubling measure. Our main result provides direct proofs of these properties by applying a Whitney covering argument and a technique inspired by the Calderón–Zygmund decomposition. In particular, this approach does not rely on reverse Hölder inequalities.