Abstract :
The reduction of the -problem on a Fr´echet nuclear space to the study of the
-operator on a Hilbert space produces a global solution u when the second
member w factors globally through this Hilbert space. Easy counterexamples show
that this global factorization is not in general possible and hence we can expect
only local factorization of w. We show that C pq1 differential forms on a
Fr´echet]Schwartz space factor locally through a normed space as C p differential
forms. The counterexamples deal with arbitrary C` differential forms w, while our
results holds for certain C` second members, in particular for all holomorphic w.
More precisely, we construct, using local solutions of usw due to Raboin and
Colombeau and Perrot, a C` solution u: EªC, when w is a holomorphic 0, 1.
form on a Fr´echet nuclear space E.
