# Iterated discrete Hardy-type inequalities with three weights for a class of matrix operators

## DOI:

https://doi.org/10.31489/2023m4/163-172## Keywords:

Inequality, discrete Lebesgue space, Hardy-type operator, weight, quasilinear operator, matrix operator## Abstract

Iterated Hardy-type inequalities are one of the main objects of current research on the theory of Hardy inequalities. These inequalities have become well-known after study boundedness properties of the multidimensional Hardy operator acting from the weighted Lebesgue space to the local Morrie-type space. In addition, the results of quasilinear inequalities can be applied to study bilinear Hardy inequalities. In the paper, we discussed weighted discrete Hardy-type inequalities containing some quasilinear operators with a matrix kernel where matrix entries satisfy discrete Oinarov condition. The research of weighted Hardy-type inequalities depends on the relations between parameters *p*, *q *and *θ*, so we considered the cases 1 *< p *≤ *q < θ < *∞ and *p *≤ *q < θ < *∞, 0 *< p *≤1, criteria for the fulfillment of iterated discrete Hardy-type inequalities are obtained. Moreover, an alternative method of proof was shown in the work.