Abstract
Discrete, continuous Hardy-type inequalities are of great importance and have numerous applications in harmonic analysis, in the theory of integral, differential and difference operators, in the theory of embeddings of function spaces and in other branches of mathematics.In recent years, weighted estimates for multidimensional Hardy-type operators have been intensively studied, which have an important application in the study of boundedness properties of operators from a Lebesgue weighted space to a local Morrey-type space, as well as in the study of bilinear operators in Lebesgue weighted spaces.The discrete case of Hardy type inequalities with three weights is an open problem.An inequality involving an iteration of the discrete Hardy operator is traditionally considered difficult to estimate because it contains three independent weight sequences and three parameters at their different ratios.In this paper we prove some new discrete iterated Hardy-type inequality involving three weights for the case 0 < p ≤ min{q, θ}.