Estimate of the best constant of discrete Hardy-type inequality with matrix operator satisfying the Oinarov condition

This paper studies the weighted inequality of Hardy-type in discrete form for matrix operators satisfying the Oinarov condition. Necessary and sufficient conditions on the weight sequences under which the Hardy-type inequality holds were found in [13] for the case $1 < p \leq q < \infty$, in [14] for the case $1 < q < p <\infty$, and in [15] for the case $0 < p \leq q < \infty$, $0 < p \leq 1$. In this paper, we extend the result of [13] with a two-sided estimate of the inequality constant.