Lower bounds of Copson type for Hausdorff matrices II

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.