The $l^p$ norms of a class of weighted mean matrices

Abstract

We study the $l^p$ norms of a class of weighted mean matrices whose diagonal terms are given by $n^{\alpha }/{\sum }_{i=1}^n{i}^{\alpha }$ with $\alpha >-1$. The $l^p$ norms of such matrices are known for $p\ge 2,(\alpha +1)p>1$ and $1<p\le 4/3,1/p\le \alpha \le 1$. In this paper, we determine the $l^p$ norms of such matrices for $p\ge 1.35,0\le \alpha \le 1$.

arXiv comment6 pages

References in corpus (1)

• Hardy-type Inequalities Via Auxiliary Sequences