发表机构
National Taiwan Normal University; University of Pittsburgh; Clemson University（台湾师范大学; 匹兹堡大学; 克莱姆森大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究改进了Hardy-Littlewood极大函数的弱型(1,1)界，通过关联热极大算子的弱型界实现，将原经典$O(n)$界优化为$O(\sqrt{n} \log n)$。
AI 中文摘要
我们针对以欧氏球为中心的Hardy-Littlewood极大函数，证明了其弱型(1,1)估计具有维度依赖关系$O(\sqrt{n} \log n)$，这改进了Stein与Strömberg经典$O(n)$估计的增长阶。证明通过将Hardy-Littlewood极大算子逐点用热极大算子界住，损失为$\sqrt{n}$；本结果的关键技术点在于将热极大算子的弱型界从$O(\sqrt{n})$改进至$O(\log n)$。
英文摘要
We prove a weak-type $(1,1)$ estimate for the centered Hardy--Littlewood maximal function with respect to Euclidean balls with dimensional dependence $O(\sqrt{n} \log n)$. This improves the order of growth in the classical $O(n)$ estimate of Stein and Strömberg. The proof goes through a pointwise bound of the Hardy--Littlewood maximal operator by the heat maximal operator with $\sqrt{n}$ loss. The key technical aspect of our result is an improvement of the weak-type bound for the heat maximal operator from $O(\sqrt{n})$ to $O(\log n)$.
Comments27 pages
