Lower bounds of Copson type for Hausdorff matrices

Let 1 p ∞, 0 < q p, and A = (an,k)n,k 0 0. Denote by Lp,q(A) the supremum of those L satisfying the following inequality: whenever and X 0. The purpose of this paper is to find the exact value of Lp,q(A) when A is a Hausdorff matrix or its transpose. In particular, we apply it to Cesàro matrices, Hölder matrices, Gamma matrices, and generalized Euler matrices. Our results generalize the work of Bennett.