  The purpose of this paper is to establish some characterizations of mixed
central Campanato space $\mathfrak{C}^{\vec{p},\lambda}(\mathbb{R}^{n})$, via
the boundedness of the commutator operators of Hardy type. Unlike the case
$\lambda\geq0$, there are some technical difficulties caused by $\lambda<0$ to
be overcome. In addition, an extra assumption called as the mixed version of
the reverse H\"{o}lder class be required in the proof of the converse
characterization. Moreover, some further interesting conclusions for the Hardy
type operators on mixed $\lambda$-central Morrey space
$\mathcal{B}^{\vec{p},\lambda}(\mathbb{R}^{n})$ are also derived.
