An RD-space 𝑀 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝑀. In this paper, firstly, the authors give the Plancherel–Pôlya characterization of product weighted Triebel–Lizorkin spaces and product weighted Besov spaces on RD-spaces and make some estimates for the product singular integral operators in Journé’s class on these function spaces. As a result of these conclusions, they present some sufficient conditions for the boundedness of product singular integral operators on the product Lipschitz spaces and product weighted Hardy spaces. Secondly, by the boundedness of lifting and projection operators, they also obtain that the dual spaces of the product weighted Hardy spaces are product weighted Carleson measure spaces. Using the idea of dual, the authors obtain the weighted boundedness of singular integral operators on the product weighted Carleson measure spaces.

中文翻译：

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Journé 类 RD 空间中乘积奇异积分算子的加权估计

RD 空间 𝑀 是 Coifman 和 Weiss 意义上的齐次类型空间，具有 𝑀 中反向加倍性质所具有的附加性质。在本文中，作者首先给出了 RD 空间上乘积加权 Triebel-Lizorkin 空间和乘积加权 Besov 空间的 Plancherel-Pôlya 表征，并对这些函数空间上 Journé 类中的乘积奇异积分算子进行了一些估计。这些结论的结果是，它们为乘积奇异积分算子在乘积 Lipschitz 空间和乘积加权 Hardy 空间上的有界性提出了一些充分条件。其次，根据提升算子和投影算子的有界性，还得出乘积加权Hardy空间的对偶空间是乘积加权Carleson测度空间。利用对偶的思想，作者获得了乘积加权卡尔森测度空间上奇异积分算子的加权有界性。