Abstract
A rearrangement inequality for the one-dimensional uncentered Hardy–Littlewood maximal function is obtained. That is, for each \(x\in {\mathbb {R}}\), the inequality \((Mf)^*(x)\le Mf^*(x)\) holds, where \(f^*\) is the symmetric decreasing rearrangement function of f. The analogical rearrangement inequalities for high-dimensional case is also studied.
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The research was supported by the National Natural Science Foundation of China (Grant Nos.11471039, 11271162 and 11871452).
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All the authors contributed equally and significantly in writing this paper. All the authors read and approved the final manuscript.
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Communicated by Jan van Neerven.
D. Yan was supported in part by National Natural Foundation of China (Grant Nos. 11561062 and 11871452).
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Nie, X., Yan, D., Liu, S. et al. Rearrangement inequality for the Hardy–Littlewood maximal operator. Banach J. Math. Anal. 16, 43 (2022). https://doi.org/10.1007/s43037-022-00197-3
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DOI: https://doi.org/10.1007/s43037-022-00197-3