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

TL;DR

This paper determines the $l^p$ norms of a specific class of weighted mean matrices for a broader range of p and alpha values, extending previous known results.

Contribution

It extends the known $l^p$ norm results for weighted mean matrices to the range $p \, \geq \, 1.35$ and $0 \, \leq \, \alpha \, \leq \, 1$, covering new parameter regimes.

Findings

Computed $l^p$ norms for $p \geq 1.35$ and $0 \leq \alpha \leq 1$

Extended previous results to broader parameter ranges

Provided explicit formulas for the norms in the new regimes

Abstract

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