Discrete H\" older and reversed Hardy-type inequalities in Lorentz sequence spaces

TL;DR

This paper develops new optimal reversed Hardy inequalities and norm estimates in Lorentz sequence spaces, leading to a sharp Hölder-type inequality for sequences.

Contribution

It introduces novel reversed Hardy inequalities and norm estimates in Lorentz sequence spaces, extending previous functional inequalities to sequence spaces.

Findings

Established optimal reversed Hardy inequalities for decreasing sequences.

Derived estimates between different Lorentz sequence space norms.

Proved a sharp Hölder-type inequality in Lorentz sequence spaces.

Abstract

We establish new optimal reversed Hardy-type inequalities on the cone of decreasing sequences from $\ell^p$-spaces with power weights, as well as estimates between different norms in Lorentz spaces of sequences. Based on these inequalities, we derive a sharp H\"older-type inequality in Lorentz sequence spaces that complements the previously considered case of functions.