Abstract
Let 1 ≤ p ≤ ∞, 0 < q ≤ p, and A = (a n,k ) n,k≥0 ≥ 0. Denote by L p,q (A) the supremum of those L satisfying the following inequality: whenever and X ≥ 0. In this article, the value distribution of L p,q (A) is determined for weighted mean matrices, Nörlund matrices and their transposes. We express the exact value of L p,q (A) in terms of the associated weight sequence. For Nörlund matrices and some kinds of transposes, this reduces to a quotient of the norms of such a weight sequence. Our results generalize the work of Bennett.
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