## Abstract

Let A(a_{n,k})_{n,k≥0} be a non-negative matrix. Denote by Lp,q(A) the supremum of those L satisfying the following inequality: The purpose of this article is to establish a Bennett-type formula for {pipe}{pipe}H^{0}{pipe}{pipe}_{p, p} and a Hardy-type formula for L_{p, p}(H^{α}_{μ}) and L_{p, p}(H^{α}_{μ}), where H^{α}_{μ} is a generalized Hausdorff matrix and 0<p≤1. Similar results are also established for L_{p, p}(H^{α}_{μ}) and L_{p, p}((H^{α}_{μ})^{t}) for other ranges of p and q. Our results extend [Chen and Wang, Lower bounds of Copson type for Hausdorff matrices, Linear Algebra Appl. 422 (2007), pp. 208-217] and [Chen and Wang, Lower bounds of Copson type for Hausdorff matrices: II, Linear Algebra Appl. 422 (2007) pp. 563-573] from H^{0}_{μ} to H^{α}_{μ} with α ≥ 0 and completely solve the value problem of {pipe}{pipe}H^{0}{pipe}{pipe}_{p, p}, L_{p, p} H^{α}_{μ}, L_{p, p} H^{α}_{μ}, and L_{p, p} ((H^{α}_{μ})^{t}) for αNU{0}.

Original language | English |
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Pages (from-to) | 321-337 |

Number of pages | 17 |

Journal | Linear and Multilinear Algebra |

Volume | 59 |

Issue number | 3 |

DOIs | |

State | Published - 1 Mar 2011 |

## Keywords

- Generalized hausdorff matrices
- Lower bound
- Operator norms