  In this paper, we give a unified construction of the recursion operators from
the Lax representation for three integrable hierarchies: Kadomtsev-Petviashvili
(KP), modified Kadomtsev-Petviashvili (mKP) and Harry-Dym under $n$-reduction.
This shows a new inherent relationship between them. To illustrate our
construction, the recursion operator are calculated explicitly for
$2$-reduction and $3$-reduction.
