A note on weighted iterated Hardy-type inequalities

Rza Mustafayev

Published 2016-06-21Version 1

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 $(0,\infty)$.