Weighted Inequalities for Discrete Iterated Hardy Operators.

We characterize a three-weight inequality for an iterated discrete Hardy-type operator. In the case when the domain space is a weighted space ℓ p with p ∈ (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 R , for all cases of involved positive exponents. [ABSTRACT FROM AUTHOR]