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Extrapolation for Weighted Product Morrey Spaces and Some Applications

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Abstract

This paper builds the extrapolation theory on weighted product Morrey spaces. To prove the main result, we introduce the weighted product block spaces which are the pre-duals of weighted product Morrey spaces and show the boundedness of the strong maximal operator on weighted product block spaces. By using this extrapolation theory, we first obtain the John-Nirenberg inequality on weighted product Morrey spaces, and then give a new characterization of little bmo in terms of weighted product Morrey spaces, which has its own interest. As applications of our extrapolation theory, we also give the Fefferman-Stein vector-valued inequalities and the mapping properties of the bi-parameter singlular integral operator and its commutator on weighted product Morrey spaces. Even in the unweighted setting, our results are new.

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Acknowledgements

The author would like to express his deep gratitude to the anonymous referees for their careful reading of the manuscript and their comments and suggestions. This work is supported by the Natural Science Foundation of Henan Province (No. 202300410338) and the Nanhu Scholar Program for Young Scholars of Xinyang Normal University.

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  1. School of Mathematics and Stastics, Xinyang Normal University, Xinyang, 464000, China

    Mingquan Wei

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Wei, M. Extrapolation for Weighted Product Morrey Spaces and Some Applications. Potential Anal 60, 445–472 (2024). https://doi.org/10.1007/s11118-022-10056-3

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