Weighted Inequalities for Discrete Iterated Hardy Operators

Abstrakt

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 is an element of (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.

Klíčová slova

• Weighted discrete inequality
• supremum operator
• iterated operator