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<p>We study the maximal operator on the variable exponent Hölder spaces in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annular decay property. Let us stress that there are no assumptions on the regularity of the variable exponent and the variable exponent can touch values 0 and 1. Furthermore, the continuity of the maximal operator between Hölder spaces is investigated. Those results are new even in the Euclidean setting.</p>

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Maximal operator in Hölder spaces

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Piotr Michał Bies,
  • Michał Gaczkowski,
  • Przemysław Górka

摘要

We study the maximal operator on the variable exponent Hölder spaces in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annular decay property. Let us stress that there are no assumptions on the regularity of the variable exponent and the variable exponent can touch values 0 and 1. Furthermore, the continuity of the maximal operator between Hölder spaces is investigated. Those results are new even in the Euclidean setting.