Abstract:
We establish necessary and sufficient conditions the validity of the discrete Hardy-type inequality
with 0 < p ≤ q < ∞ and 0 < p ≤ 1, where the matrices (ai,j ) is an arbitrary matrix and the entries
of the matrix (ai,j ) ≥ 0 such that ai,j is non-increasing in the second index. Also some further
results are pointed out on the cone of monotone sequences. Moreover, we give that the applications
of the main results for the non-negative and triangular matrices (ai,j ≥ 0 for 1 ≤ j ≤ i and ai,j =
0 for i < j).
