  Let H be a separable real Hilbert space and let F = (F_t)_{t\in [0,T]} be the
augmented filtration generated by an H-cylindrical Brownian motion W_H on
[0,T]. We prove that if E is a UMD Banach space, 1\leq p<\infty, and f\in
D^{1,p}(E) is F_T-measurable, then f = \E f + \int_0^T P_F(Df) dW_H where D is
the Malliavin derivative and P_F is the projection onto the F-adapted elements
in a suitable Banach space of L^p-stochastically integrable L(H,E)-valued
processes.
