TY - JOUR

T1 - Lower bounds of Copson type for weighted mean matrices and Nörlund matrices

AU - Chen, Chang Pao

AU - Wang, Kuo-Zhong

PY - 2010/4/1

Y1 - 2010/4/1

N2 - Let 1 ≤ p ≤ ∞, 0 < q ≤ p, and A = (an,k)n,k≥0 ≥ 0. Denote by Lp,q(A) the supremum of those L satisfying the following inequality: whenever and X ≥ 0. In this article, the value distribution of Lp,q(A) is determined for weighted mean matrices, Norlund matrices and their transposes. We express the exact value of Lp,q(A) in terms of the associated weight sequence. For Norlund matrices and some kinds of transposes, this reduces to a quotient of the norms of such a weight sequence. Our results generalize the work of Bennett.

AB - Let 1 ≤ p ≤ ∞, 0 < q ≤ p, and A = (an,k)n,k≥0 ≥ 0. Denote by Lp,q(A) the supremum of those L satisfying the following inequality: whenever and X ≥ 0. In this article, the value distribution of Lp,q(A) is determined for weighted mean matrices, Norlund matrices and their transposes. We express the exact value of Lp,q(A) in terms of the associated weight sequence. For Norlund matrices and some kinds of transposes, this reduces to a quotient of the norms of such a weight sequence. Our results generalize the work of Bennett.

KW - Lower bound

KW - Norlund matrices

KW - Weighted mean matrices

UR - http://www.scopus.com/inward/record.url?scp=77951200028&partnerID=8YFLogxK

U2 - 10.1080/03081080802614196

DO - 10.1080/03081080802614196

M3 - Article

AN - SCOPUS:77951200028

VL - 58

SP - 343

EP - 353

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 3

ER -