On $l^p$ norms of factorable matrices

TL;DR

This paper investigates the $l^p$ operator norms of factorable matrices, providing new insights and applications to weighted mean matrices, Copson's inequalities, and the Hardy-Littlewood-Pólya inequality constants.

Contribution

It introduces a novel method to analyze $l^p$ norms of factorable matrices and applies it to various classical inequalities and matrix classes.

Findings

Derived new bounds for $l^p$ operator norms of weighted mean matrices

Established results on Copson's inequalities using the proposed method

Determined the best constant in a classical Hardy-Littlewood-Pólya inequality

Abstract

We study $l^p$ operator norms of factorable matrices and related results. We give applications to $l^p$ operator norms of weighted mean matrices and Copson's inequalities. We also apply the method in this paper to study the best constant in an inequality of Hardy, Littlewood and P\'{o}lya.