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<p>The purpose of this paper is threefold. First, we introduce product Morrey-Herz spaces and product block-Herz spaces, establish their duality, and prove the boundedness of the strong maximal operator on product block-Herz spaces; these results provide the foundation for extrapolation. Second, using the Rubio de Francia iteration method, we establish extrapolation results on product Morrey-Herz spaces. Finally, we give applications to Fefferman-Stein vector-valued strong maximal inequalities, the John-Nirenberg inequality, a characterization of little bmo in terms of product Morrey-Herz spaces, and the boundedness of bi-parameter Calderón-Zygmund operators and their commutators.</p>

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Extrapolation to product Morrey-Herz spaces and applications

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Xi Cen,
  • Zichen Song

摘要

The purpose of this paper is threefold. First, we introduce product Morrey-Herz spaces and product block-Herz spaces, establish their duality, and prove the boundedness of the strong maximal operator on product block-Herz spaces; these results provide the foundation for extrapolation. Second, using the Rubio de Francia iteration method, we establish extrapolation results on product Morrey-Herz spaces. Finally, we give applications to Fefferman-Stein vector-valued strong maximal inequalities, the John-Nirenberg inequality, a characterization of little bmo in terms of product Morrey-Herz spaces, and the boundedness of bi-parameter Calderón-Zygmund operators and their commutators.