Article ID Journal Published Year Pages File Type
4603519 Linear Algebra and its Applications 2007 11 Pages PDF
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:∑n=0∞∑k=0∞an,kxkq1/q⩾L∑k=0∞xkp1/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(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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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