Lower bounds of Copson type for Hausdorff matrices

Chang Pao Chen*, Kuo-Zhong Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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:fenced(underover(∑, n = 0, ∞) fenced(underover(∑, k = 0, ∞) an, k xk)q)1 / q ≥ L fenced(underover(∑, k = 0, ∞) xkp)1 / p,whenever X = {xn}n = 0 ∈ ℓp and X ≥ 0. The purpose of this paper is to find the exact value of Lp,q(A) when A is a Hausdorff matrix or its transpose. In particular, we apply it to Cesàro matrices, Hölder matrices, Gamma matrices, and generalized Euler matrices. Our results generalize the work of Bennett.

Original languageEnglish
Pages (from-to)208-217
Number of pages10
JournalLinear Algebra and Its Applications
Volume420
Issue number1
DOIs
StatePublished - 1 Jan 2007

Keywords

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

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