Criteria on boundedness of matrix operators in weighted spaces of sequences and their applications

Hardy-type inequalities for matrix operators

“…The inequalities (1) and (2) have been investigated for the case 0 < p, q < ∞ with a triangular matrix (a i,j ≥ 0 for 1 ≤ j ≤ i and a i,j = 0 for i < j) in [2][3][4][5] and the references given therein. However, these inequalities have not been studied for the case 0 < p ≤ q < ∞ and p ≤ 1.…”

“…The main aim of this paper is to investigate that the problems necessary and sufficient conditions the validity of inequalities (1) and (2) with the case 0 < p ≤ q < ∞, 0 < p < 1 and under weaker conditions on the matrices (a i,j ) in operators defined by (3) and (4) for all sequences f ≥ 0 (see theorems 2.1-2.2). Moreover, we study these problems on the cone of monotone sequences (see theorems 2.3-2.6).…”