  We prove extension of a di-bar-closed, smooth, form from the intersection of
a pseudoconvex domain with a complex hyperplane to the whole domain. The
extension form is di-bar-closed, has harmonic coefficients and its L^2-norm is
estimated by the L^2-norm of the trace. For holomorphic functions this is
proved by Ohsawa-Takegoshi [12]. For forms of higher degree, this is stated by
Manivel [9]. It seems, however, that the proof contains a gap because of the
use of a a singular weight and the failure of regularity for the solution of
the related di-bar-equation.
  There is a rich literature on the subject (cf. among otheres [7], [14]) but
it does not seem to contain complete answer to the question. Also, the problem
of extending cohomology classes of di-bar of higher degree in a compact Kahler
space is addressed in [8] and [3]. Apart from the formal analogy, this has
little in common with our problem in which these classes are 0. We also
believe, comparing to the preceding literature, that our approach is original
and, somewhat, simpler.
