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<p>We introduce Riesz potentials for Lebesgue non-measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results for these operators. Some earlier results are recovered or extended now using integrals taken in the sense of Choquet with respect to Hausdorff content. Some earlier results also for maximal operators are considered, but now for Lebesgue non-measurable functions.</p>

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On Hausdorff content maximal operator and Riesz potential for non-measurable functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月9日

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  • Petteri Harjulehto,
  • Ritva Hurri-Syrjänen

摘要

We introduce Riesz potentials for Lebesgue non-measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results for these operators. Some earlier results are recovered or extended now using integrals taken in the sense of Choquet with respect to Hausdorff content. Some earlier results also for maximal operators are considered, but now for Lebesgue non-measurable functions.