Abstract
In this paper, we obtain characterizations of the boundedness of multivariate weighted Hardy-type operators on monotone functions. We also study properties of the weight functions u on \(ℝ_ + ^n\) satisfying the condition \(B_p^{\overrightarrow \phi }\left( {ℝ_ + ^n} \right)\), which is an extension of the well-known conditions Bp and \({B_p}\left( {ℝ_ + ^n} \right)\). Finally, we give simpler characterizations of the boundedness of Hardy-type operators when the weight u admits the separation of variables.
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Acknowledgments
The authors are grateful to the referee for valuable suggestions which helped to improve the presentation of the paper.
Funding
This work was supported by the Natural Science Foundation of Zhejiang Province of China under grant no. LY19A010001 and by the National Natural Science Foundation of China under grant no. 11961056.
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Sun, Q., Li, H. Weighted Hardy-Type Operators on Nonincreasing Cones. Math Notes 107, 1002–1013 (2020). https://doi.org/10.1134/S0001434620050326
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DOI: https://doi.org/10.1134/S0001434620050326