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Estimates for the Product Weighted Hardy–Littlewood Average and Its Commutator on Product Central Morrey Spaces

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Abstract

We study the product weighted Hardy–Littlewood average \(\mathcal {H}_{\varphi }\) in this paper. More precisely, we first give the sufficient and necessary condition for the boundedness of \(\mathcal {H}_{\varphi }\) on the product central Morrey space \(\vec {\dot{B}}^{p,\lambda }(\mathbb {R}^n\times \mathbb {R}^m)\), and obtain the sharp constant at the same time. Then we obtain a characterization of the boundedness for the commutator formed by \(\mathcal {H}_{\varphi }\) and a product central bounded mean oscillation function b. As a consequence, we give a complete answer to a question posed by Fu et al. (Forum Math 27(5):2825–2851, 2015).

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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 Statistics, Xinyang Normal University, Xinyang, 464000, People’s Republic of China

    Mingquan Wei

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Wei, M. Estimates for the Product Weighted Hardy–Littlewood Average and Its Commutator on Product Central Morrey Spaces. Mediterr. J. Math. 18, 235 (2021). https://doi.org/10.1007/s00009-021-01876-5

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