  An n-tuple (n \geq 2), T = (T_1, \ldots, T_n), of commuting bounded linear
operators on a Hilbert space \mathcal{H} is doubly commuting if T_i T_j^* =
T_j^* T_i for all $1 \leq i < j \leq n$. If in addition, each T_i \in C_{\cdot
0}, then we say that T is a doubly commuting pure tuple. In this paper we prove
that a doubly commuting pure tuple $T$ can be dilated to a tuple of shift
operators on some suitable vector-valued Hardy space
H^2_{\mathcal{D}_{T^*}}(\mathbb{D}^n). As a consequence of the dilation
theorem, we prove that there exists a closed subspace \mathcal{S}_T of the form
\[\mathcal{H}_{T} := \sum_{i=1}^n \Phi_{T_i}
H^2_{\mathcal{E}_{T_i}}(\mathbb{D}^n),\] where \{\mathcal{E}_{T_i}\}_{i=1}^n
are Hilbert spaces, \Phi_{T_i} \in H^\infty_{\mathcal{B}(\mathcal{E}_{T_i},
\mathcal{D}_{T^*})}(\mathbb{D}^n) such that each \Phi_{T_i} (1 \leq i \leq n)
is either a one variable inner function in z_i, or the zero function. Moreover,
\mathcal{H} \cong \mathcal{S}_T^\perp and \[(T_1, \ldots, T_n) \cong
P_{\mathcal{S}_T^\perp} (M_{z_1}, \ldots, M_{z_n})|_{\mathcal{S}_T^\perp}.\]
