Let \(({{\mathcal {X}}},d,\mu )\) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we first establish several weighted norm estimates for various maximal functions. Then we show the weighted boundedness of the fractional integral \(I_\beta \) associated with admissible functions and its commutators. Similarly to \(I_\beta \), corresponding results for Calderón–Zygmund operators T associated with admissible functions are also included in this article.

中文翻译：

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与齐次类型空间上的容许函数相关的分数积分的加权有界性

令 \(({{\mathcal {X}}},d,\mu )\) 为 Coifman 和 Weiss 意义上的齐次类型空间。在本文中，我们首先为各种最大函数建立几个加权范数估计。然后我们展示与容许函数及其交换子相关的分数积分 \(I_\beta \) 的加权有界性。与 \(I_\beta \) 类似，本文还包含与容许函数相关的 Calderón–Zygmund 算子 T 的相应结果。