Operator norms and lower bounds of generalized Hausdorff matrices.

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: [image omitted] The purpose of this article is to establish a Bennett-type formula for [image omitted] and a Hardy-type formula for [image omitted] and [image omitted], where [image omitted] is a generalized Hausdorff matrix and 0 < p ≤ 1. Similar results are also established for [image omitted] and [image omitted] 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 [image omitted] to [image omitted] with α ≥ 0 and completely solve the value problem of [image omitted], [image omitted], [image omitted] and [image omitted] for α ∈  ∪ {0}. [ABSTRACT FROM AUTHOR]