Extensions of Hardy inequality

Matrices Whose Norms Are Determined by Their Actions on Decreasing Sequences

“…Bennett established this upper bound equality for the case that E = F = ℓ p , 1 < p < ∞, and A is a weighted mean matrix with decreasing weights w n [2, p. 422], [3, p. 422]. This result was extended by Jameson [6,Theorem 2] to the case that E = F is a Banach lattice of sequences with property (PS) and A satisfies the following condition: In [5,Lemma 2.4], the first author extended Bennett's result to the case A ℓ p ,ℓ p = A ℓ p ,ℓ p ,↓ , where 1 < p < ∞ and A is a non-negative lower triangular matrix with rows decreasing in the sense that a j,k ≥ a j,k+1 for all j, k ≥ 1. Jameson and Lashkaripour [8, Lemma 2.1] established the equality…”

Bounds for the norm of lower triangular matrices on the Cesàro weighted sequence space

“…In the study, we will expand this problem for matrix operators from into and matrix operators from into , and we consider certain matrix operators such as Cesàro, Nörlund and weighted mean. The study is an extension of some results obtained by [3, 7]. …”

“…Moreover, we computed the norms of certain matrix operators such as Cesàro, Nörlund and weighted mean, and we extended some results of [3, 7]. …”

Lower bounds of Copson type for the transposes of lower triangular matrices

“…This matrix is closely related to the matrix C N appeared in [5,Lemma 2.3]. For N = 1, C 1 N reduces to the Cesàro matrix C(1).…”