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arXiv · 2402.12321

Extrapolation to product Morrey-Herz spaces and applications

Xi Cen·Zichen Song
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Abstract

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 Calder\'on-Zygmund operators and their commutators.

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Xi Cen, Zichen Song. 2024-02-19. Extrapolation to product Morrey-Herz spaces and applications. https://doi.org/10.1007/s13226-026-00998-4

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