  We study a three-weight inequality for the superposition of the Hardy
operator and the Copson operator, namely \begin{equation*}
  \bigg(\int_a^b \bigg(\int_t^b \bigg(\int_a^s f(\tau)^p v(\tau) \,d\tau
\bigg)^\frac{q}{p} u(s) \,ds \bigg)^{\frac{r}{q}} w(t) \,dt
\bigg)^{\frac{1}{r}} \leq C \int_a^b f(t)\,dt, \end{equation*} in which $(a,b)$
is any nontrivial interval, $q,r$ are positive real parameters and $p\in(0,1]$.
A simple change of variables can be used to obtain any weighted $L^p$-norm with
$p\ge1$ on the right-hand side. Another simple change of variables can be used
to equivalently turn this inequality into the one in which the Hardy and Copson
operators swap their positions. We focus on characterizing those triples of
weight functions $(u,v,w)$ for which this inequality holds for all nonnegative
measurable functions $f$ with a constant independent of $f$.
  We use a new type of approach based on an innovative method of discretization
which enables us to avoid duality techniques and therefore to remove various
restrictions that appear in earlier work.
  This paper is dedicated to Professor Stefan Samko on the occasion of his 80th
birthday.
