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 language | English |
---|---|
Pages (from-to) | 563-573 |
Number of pages | 11 |
Journal | Linear Algebra and Its Applications |
Volume | 422 |
Issue number | 2-3 |
DOIs | |
State | Published - 15 Apr 2007 |
Keywords
- Cesàro matrices
- Gamma matrices
- Generalized Euler matrices
- Hausdorff matrices
- Hölder matrices
- Lower bound