A NOTE ON lp 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 Weighted Composition Operators on L^p-Spaces

A note on l norms of weighted mean matrices

Correspondence: penggao@ntu. edu.sg Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore Abstract We present some results concerning the l norms of weighted mean matrices. These results can be regarded as analogues to a result of Bennett concerning weighted Carleman’s inequalities. 2000 Mathematics Subject Classifica...

On Weighted Remainder Form of Hardy-type Inequalities

∣ p . Hardy’s inequality thus asserts that the Cesáro matrix operator C = (cj,k), given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ p/(p − 1). (The norm is in fact p/(p − 1).) Hardy’s inequality leads naturally to the study on lp norms of general matrices. For example, we say a matrix A = (aj,k) is a weighted mean matrix if its entries satisfy aj,k = 0, k > j and aj,k ...

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...