Lower bounds of Copson type for Hausdorff matrices II

Chang Pao Chen; Kuo-Zhong Wang

doi:10.1016/j.laa.2006.11.015

Lower bounds of Copson type for Hausdorff matrices II

Chang Pao Chen^*, Kuo-Zhong Wang

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article

13 Scopus citations

Abstract

Let A = (a_n,k)_n,k≥0 be a non-negative matrix. Denote by L_p,q(A) the supremum of those L satisfying the following inequality:{Mathematical expression}The purpose of this paper is to establish a Hardy-type formula for L_p,q(H_μ), where H_μ is a Hausdorff matrix and 0 < q ≤ p ≤ 1. A similar result is also established for L_{p, q} (H_μ^t) with -∞ < q ≤ p < 0. As a consequence, we apply them to Cesàro matrices, Hölder matrices, Gamma matrices, generalized Euler matrices, and Hausdorff matrices with monotone rows. Our results fill up the gap which the work of Bennett has not dealt with.

Original language	English
Pages (from-to)	563-573
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	422
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2006.11.015
State	Published - 15 Apr 2007

Keywords

Cesàro matrices
Gamma matrices
Generalized Euler matrices
Hausdorff matrices
Hölder matrices
Lower bound

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10.1016/j.laa.2006.11.015

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Chen, C. P., & Wang, K-Z. (2007). Lower bounds of Copson type for Hausdorff matrices II. Linear Algebra and Its Applications, 422(2-3), 563-573. https://doi.org/10.1016/j.laa.2006.11.015

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title = "Lower bounds of Copson type for Hausdorff matrices II",

abstract = "Let A = (an,k)n,k≥0 be a non-negative matrix. Denote by Lp,q(A) the supremum of those L satisfying the following inequality:{Mathematical expression}The purpose of this paper is to establish a Hardy-type formula for Lp,q(Hμ), where Hμ is a Hausdorff matrix and 0 < q ≤ p ≤ 1. A similar result is also established for Lp, q (Hμt) with -∞ < q ≤ p < 0. As a consequence, we apply them to Ces{\`a}ro matrices, H{\"o}lder matrices, Gamma matrices, generalized Euler matrices, and Hausdorff matrices with monotone rows. Our results fill up the gap which the work of Bennett has not dealt with.",

keywords = "Ces{\`a}ro matrices, Gamma matrices, Generalized Euler matrices, Hausdorff matrices, H{\"o}lder matrices, Lower bound",

author = "Chen, {Chang Pao} and Kuo-Zhong Wang",

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T1 - Lower bounds of Copson type for Hausdorff matrices II

AU - Chen, Chang Pao

AU - Wang, Kuo-Zhong

PY - 2007/4/15

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N2 - Let A = (an,k)n,k≥0 be a non-negative matrix. Denote by Lp,q(A) the supremum of those L satisfying the following inequality:{Mathematical expression}The purpose of this paper is to establish a Hardy-type formula for Lp,q(Hμ), where Hμ is a Hausdorff matrix and 0 < q ≤ p ≤ 1. A similar result is also established for Lp, q (Hμt) with -∞ < q ≤ p < 0. As a consequence, we apply them to Cesàro matrices, Hölder matrices, Gamma matrices, generalized Euler matrices, and Hausdorff matrices with monotone rows. Our results fill up the gap which the work of Bennett has not dealt with.

AB - Let A = (an,k)n,k≥0 be a non-negative matrix. Denote by Lp,q(A) the supremum of those L satisfying the following inequality:{Mathematical expression}The purpose of this paper is to establish a Hardy-type formula for Lp,q(Hμ), where Hμ is a Hausdorff matrix and 0 < q ≤ p ≤ 1. A similar result is also established for Lp, q (Hμt) with -∞ < q ≤ p < 0. As a consequence, we apply them to Cesàro matrices, Hölder matrices, Gamma matrices, generalized Euler matrices, and Hausdorff matrices with monotone rows. Our results fill up the gap which the work of Bennett has not dealt with.

KW - Cesàro matrices

KW - Gamma matrices

KW - Generalized Euler matrices

KW - Hausdorff matrices

KW - Hölder matrices

KW - Lower bound

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