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arXiv · 1903.04313

Weighted inequalities for discrete iterated Hardy operators

Amiran Gogatishvili·Martin Křepela·Rastislav Oľhava·Luboš Pick
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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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Amiran Gogatishvili, Martin Křepela, Rastislav Oľhava, Luboš Pick. 2019-03-11. Weighted inequalities for discrete iterated Hardy operators. https://arxiv.org/abs/1903.04313

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