Lower bounds of Copson type for Hausdorff matrices II

Chang Pao Chen*, Kuo-Zhong Wang

*Corresponding author for this work

Research output: Contribution to journalArticle

13 Scopus citations

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 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 languageEnglish
Pages (from-to)563-573
Number of pages11
JournalLinear Algebra and Its Applications
Volume422
Issue number2-3
DOIs
StatePublished - 15 Apr 2007

Keywords

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

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