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<p>In this paper, we establish a complete characterization of the necessary and sufficient conditions for the boundedness of fractional integral operators along the diagonal from mixed Morrey spaces to weak Morrey spaces. The main approach is based on exploiting two dualities: one between mixed-norm Morrey spaces and function spaces associated with Hausdorff capacities, and the other between weak Morrey spaces and block spaces. This framework is further combined with the construction of specific functions to rigorously establish the necessity of the conditions.</p>

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Boundedness of the fractional integral operator on mixed Morrey spaces

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Jiheng Tan,
  • Fayou Zhao

摘要

In this paper, we establish a complete characterization of the necessary and sufficient conditions for the boundedness of fractional integral operators along the diagonal from mixed Morrey spaces to weak Morrey spaces. The main approach is based on exploiting two dualities: one between mixed-norm Morrey spaces and function spaces associated with Hausdorff capacities, and the other between weak Morrey spaces and block spaces. This framework is further combined with the construction of specific functions to rigorously establish the necessity of the conditions.