A note on l norms of weighted mean matrices

ON WEIGHTED MEAN MATRICES WHOSE lp NORMS ARE DETERMINED ON DECREASING SEQUENCES

We give a condition on weighted mean matrices so that their l norms are determined on decreasing sequences when the condition is satisfied. We apply our result to give a proof of a conjecture of Bennett and discuss some related results.

A NOTE ON lp NORMS OF WEIGHTED MEAN MATRICES

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...

A Note on Weighted Composition Operators on L^p-Spaces

Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...

NORMS OF MATRIX OPERATORS ON bvp

In this paper we consider the problem of finding norms of certain matrix operators on sequence space bvp . In fact, we consider these problems for weighted mean, and generalized Cesaro matrices on sequence space bvp . Mathematics subject classification (2010): 26D15, 47A30, 40G05, 47D37, 46A45, 54D55.