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<p>In this paper, we introduce a class of abstract measure Morrey spaces associated with the ball-basis structure. Their predual spaces are characterized and an interpolation theorem is established. The boundedness of the Hardy-Littlewood maximal operator and sparse operators is also obtained. Moreover, the study of bounded oscillation operators provides a unified perspective on several fundamental operators in harmonic analysis, including Calderón-Zygmund operators on spaces of homogeneous type, Littlewood-Paley square operators, higher order Calderón commutators, Carleson-type operators, and the Hardy-Littlewood maximal operator. As an application, we obtain the boundedness of these operators on Morrey spaces over spaces of homogeneous type.</p>

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Abstract Measure Morrey Spaces with Ball-Basis and their Applications

  • 期刊论文

  • 发表日期：

    2026年1月30日

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  • Fate Shan,
  • Qingying Xue,
  • Jiang Zhou

摘要

In this paper, we introduce a class of abstract measure Morrey spaces associated with the ball-basis structure. Their predual spaces are characterized and an interpolation theorem is established. The boundedness of the Hardy-Littlewood maximal operator and sparse operators is also obtained. Moreover, the study of bounded oscillation operators provides a unified perspective on several fundamental operators in harmonic analysis, including Calderón-Zygmund operators on spaces of homogeneous type, Littlewood-Paley square operators, higher order Calderón commutators, Carleson-type operators, and the Hardy-Littlewood maximal operator. As an application, we obtain the boundedness of these operators on Morrey spaces over spaces of homogeneous type.