Factorizations of weighted Hardy inequalities

TL;DR

This paper develops factorizations of weighted Hardy inequalities, improving existing bounds by analyzing weighted Lebesgue, Cesàro, and Copson spaces under specific weight conditions to ensure the Hardy operator's boundedness.

Contribution

It introduces new factorizations of weighted Hardy inequalities that extend and improve upon the best known forms for weighted Lebesgue, Cesàro, and Copson spaces.

Findings

Enhanced bounds for weighted Hardy inequalities

New factorizations for weighted Lebesgue, Cesàro, and Copson spaces

Conditions ensuring Hardy operator boundedness

Abstract

We present factorizations of weighted Lebesgue, Ce\-s\` aro and Copson spaces, for weights satisfying the conditions which assure the boundedness of the Hardy's integral operator between weighted Lebesgue spaces. Our results enhance, among other, the best known forms of weighted Hardy inequalities.