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

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arxiv 2405.12113 v1 pith:YCLL3ZGC submitted 2024-05-20 math.FA

Petteri Harjulehto , Ritva Hurri-Syrjänen This is my paper · ORCID
classification math.FA
keywords contentfunctionshausdorffresultschoquetearlierintegralsmaximal
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We introduce Riesz potentials for non-Lebesgue 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 non-measurable functions.

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  1. Uncentered Fractional Maximal functions and mean oscillation spaces associated with dyadic Hausdorff content

    math.FA 2025-06 conditional novelty 8.0 of 10

    Fractional maximal operators map BMO functions into Hausdorff-content BLO spaces, send BMO to VMO via uniform continuity, and preserve vanishing mean oscillation spaces adapted to dyadic Hausdorff content.

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