Lower bounds of Copson type for Hausdorff matrices II
In: Linear algebra and its applications, Jg. 422 (2007), Heft 2-3, S. 563-573
Online
academicJournal
- print, 9 ref
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: (∞Σn=0(∞Σn=0 an,kxk)q)1/q ≥ L(∞Σk=0xkp)1/p (X ∈ ℓp, X≥0). 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(Htμ) with -oo < g ≤ p < 0. As a consequence, we apply them to Cesàro matrices, Holder 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.
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Lower bounds of Copson type for Hausdorff matrices II
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Autor/in / Beteiligte Person: | CHEN, Chang-Pao ; WANG, Kuo-Zhong |
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Zeitschrift: | Linear algebra and its applications, Jg. 422 (2007), Heft 2-3, S. 563-573 |
Veröffentlichung: | New York, NY: Elsevier Science, 2007 |
Medientyp: | academicJournal |
Umfang: | print, 9 ref |
ISSN: | 0024-3795 (print) |
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