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Weighted Inequalities for Discrete Iterated Hardy Operators
Mediterranean Journal of Mathematics ( IF 1.1 ) Pub Date : 2020-08-01 , DOI: 10.1007/s00009-020-01526-2 Amiran Gogatishvili , Martin Křepela , Rastislav OĽhava , Luboš Pick
Mediterranean Journal of Mathematics ( IF 1.1 ) Pub Date : 2020-08-01 , DOI: 10.1007/s00009-020-01526-2 Amiran Gogatishvili , Martin Křepela , Rastislav OĽhava , Luboš Pick
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:
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。
更新日期:2020-08-01
中文翻译:
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。