On l p norms of weighted mean matrices
نویسندگان
چکیده
منابع مشابه
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...
متن کاملON 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...
متن کاملA 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...
متن کاملON l2 NORMS OF SOME WEIGHTED MEAN MATRICES
k=1 |ak|, in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ ...
متن کاملA NOTE ON l2 NORMS OF WEIGHTED MEAN MATRICES
k=1 |ak| , in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2009
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-009-0490-2