ON lp NORMS OF WEIGHTED MEAN MATRICES
نویسنده
چکیده
p . It follows that inequality (1.2) holds for any a ∈ lp when U1/p ≥ ||C||p,p and fails to hold for some a ∈ lp when U1/p < ||C||p,p. Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cn,k = 1/n, k ≤ n and 0 otherwise, is bounded on l p and has norm ≤ p/(p−1). (The norm is in fact p/(p− 1).) We say a matrix A = (an,k) is a lower triangular matrix if an,k = 0 for n < k and a lower triangular matrix A is a summability matrix if an,k ≥ 0 and ∑n k=1 an,k = 1. We say a summability matrix A is a weighted mean matrix if its entries satisfy: (1.3) an,k = λk/Λn, 1 ≤ k ≤ n; Λn = n ∑
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