Corrigendum to "On weighted iterated Hardy-type inequalities" [Positivity, 22 (1) (2018), 275-299]

TL;DR

This paper corrects a previous mistake in the characterization of a complex weighted iterated Hardy-type inequality involving multiple integrals and weight functions.

Contribution

It provides a corrected and precise characterization of a specific weighted iterated Hardy-type inequality from a prior publication.

Findings

Corrected the inequality characterization from the original paper.

Clarified conditions on weight functions for the inequality to hold.

Enhanced understanding of weighted Hardy-type inequalities.

Abstract

We correct a mistake in the paper ["On weighted iterated Hardy-type inequalities", Positivity, 22 (1) (2018), 275-299]. -- In this paper the inequality $$ \bigg( \int_0^{\infty} \bigg( \int_x^{\infty} \bigg( \int_t^{\infty} h \bigg)^q w(t)\,dt \bigg)^{r / q} u(x)\,ds \bigg)^{1/r}\leq C \,\int_0^{\infty} h v, \quad h \in {\mathfrak M}^+(0,\infty) $$ is characterized. Here $0 < q ,\, r < \infty$ and $u,\,v,\,w$ are weight functions on $(0,\infty)$.