Abstract
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.
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We would like to thank the referee for a very thorough and critical reading of the paper and for numerous suggestions for improvements.
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This research was supported by the Grants P201-13-14743S and P201-18-00580S of the Czech Science Foundation and by the Grant 8X17028 of the Czech Ministry of Education. The research of A. Gogatishvili was partially supported by Shota Rustaveli National Science Foundation (SRNSF), Grant no: FR17-589.
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Gogatishvili, A., Křepela, M., OĽhava, R. et al. Weighted Inequalities for Discrete Iterated Hardy Operators. Mediterr. J. Math. 17, 132 (2020). https://doi.org/10.1007/s00009-020-01526-2
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DOI: https://doi.org/10.1007/s00009-020-01526-2