### Abstract

Let A = (a_{n,k})_{n,k≥0} be a non-negative matrix. Denote by L_{p,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 L_{p,q}(H_{μ}), where H_{μ} is a Hausdorff matrix and 0 < q ≤ p ≤ 1. A similar result is also established for L_{p, q} (H_{μ}^{t}) 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 |
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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

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## Cite this

Chen, C. P., & Wang, K-Z. (2007). Lower bounds of Copson type for Hausdorff matrices II.

*Linear Algebra and Its Applications*,*422*(2-3), 563-573. https://doi.org/10.1016/j.laa.2006.11.015