2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156001Let 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.12 pages; revised version, to appear in Electronic Communications in ProbabilityProbabilityFunctional Analysis60H07 (Primary); 46B09, 60H05 (Secondary)text