We characterize a three-weight inequality for an iterated discrete Hardy-type operator. In the case when the domain space is a weighted space \(\ell ^{p}\) with \(p\in (0,1]\), we develop characterizations which enable us to reduce the problem to another one with \(p=1\). This, in turn, makes it possible to establish an equivalence of the weighted discrete inequality to an appropriate inequality for iterated Hardy-type operators acting on measurable functions defined on \({\mathbb {R}}\), for all cases of involved positive exponents.

中文翻译：

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离散迭代Hardy算子的加权不等式

我们刻画了一个迭代的离散Hardy型算子的三重不等式。在域空间是具有\（p \ in（0,1] \）的加权空间\（\ ell ^ {p} \）的情况下，我们开发了一些表征，这些特征使我们可以将问题简化为\ （p = 1 \），这反过来使得有可能建立加权离散不等式到适当的不等式的等价性，这些不等式适用于作用于\（{\ mathbb {R}} \ ），适用于所有涉及正指数的情况。