  Let $1\leq p <\infty$ and $0 < q,r < \infty$. We characterize validity of the
inequality for the composition of the Hardy operator, \begin{equation*}
\bigg(\int_a^b \bigg(\int_a^x \bigg(\int_a^t f(s)ds \bigg)^q u(t) dt
\bigg)^{\frac{r}{q}} w(x) dx \bigg)^{\frac{1}{r}} \leq C \bigg(\int_a^b f^p(x)
v(x) dx \bigg)^{\frac{1}{p}} \end{equation*} for all non-negative measurable
functions on $(a,b)$, $-\infty \leq a < b \leq \infty$. We construct a more
straightforward discretization method than those previously presented in the
literature, and we characterize this inequality in both discrete and continuous
forms.
