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A WEIGHTED MAXIMAL WEAK‐TYPE INEQUALITY
Mathematika ( IF 0.8 ) Pub Date : 2020-12-02 , DOI: 10.1112/mtk.12065 Adam Osȩkowski 1 , Mateusz Rapicki 1
Mathematika ( IF 0.8 ) Pub Date : 2020-12-02 , DOI: 10.1112/mtk.12065 Adam Osȩkowski 1 , Mateusz Rapicki 1
Affiliation
Let w be a dyadic weight ( ), and let be the dyadic Hardy–Littlewood maximal function on . The paper contains the proof of the estimate
where the constant does not depend on the dimension d. Furthermore, the linear dependence on is optimal, which is a novel result for . The estimate is shown to hold in a wider context of probability spaces equipped with an arbitrary tree‐like structure. The proof rests on the Bellman function method: we construct an abstract special function satisfying certain size and concavity requirements.
中文翻译:
加权的最大弱型不等式
让W¯¯是二进 重量( ), 然后让 成为上的二元Hardy–Littlewood最大函数 。该文件包含估计的证明
常数 不依赖于尺寸d。此外,对 是最优的,这对于 。结果表明,该估计值在配备有任意树状结构的概率空间的更广泛上下文中保持有效。证明基于Bellman函数方法:我们构造了一个满足特定大小和凹度要求的抽象特殊函数。
更新日期:2020-12-03
中文翻译:
加权的最大弱型不等式
让W¯¯是二进 重量( ), 然后让 成为上的二元Hardy–Littlewood最大函数 。该文件包含估计的证明