遍历理论中的 $A_\infty$ 权重特征

Wei Chen, Jingyi Wang
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引用次数: 0

摘要

我们从遍历理论中二元网格的角度出发,建立了离散加权版的 Calder\'{o}n-Zygmund 分解。基于该分解,我们研究了离散 $A_\infty$ 权重。首先,我们得到了反向 H\"{o}lder 不等式的特征及其扩展。其次,给出了 $A_infty$ 的性质,特别是 $A_infty$ 蕴涵反向 H\"{o}lder 不等式。最后,在权重的加权条件下,$A_infty$ 来自反向 H\"{o}lder 正弦不等式。这意味着我们得到了$A_{\infty}$的等价特征。因为 $A_{infty}$ 暗含加倍条件,所以假设这个条件似乎是合理的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Characterizations of $A_\infty$ Weights in Ergodic Theory
We establish a discrete weighted version of Calder\'{o}n-Zygmund decomposition from the perspective of dyadic grid in ergodic theory. Based on the decomposition, we study discrete $A_\infty$ weights. First, characterizations of the reverse H\"{o}lder's inequality and their extensions are obtained. Second, the properties of $A_\infty$ are given, specifically $A_\infty$ implies the reverse H\"{o}lder's inequality. Finally, under a doubling condition on weights, $A_\infty$ follows from the reverse H\"{o}lder's inequality. This means that we obtain equivalent characterizations of $A_{\infty}$. Because $A_{\infty}$ implies the doubling condition, it seems reasonable to assume the condition.
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