  We first show that the canonical solution operator to d-bar restricted to
(0,1)-forms with holomorphic coefficients can be expressed by an integral
operator using the Bergman kernel. This result is used to prove that in the
case of the unit disc in C the canonical solution operator to d-bar restricted
to (0,1)-forms with holomorphic coefficients is a Hilbert-Schmidt operator. In
the sequel we give a direct proof of the last statement using orthonormal bases
and show that in the case of polydisc and the unit ball in C^n, n>1, the
corresponding operator fails to be a Hilbert-Schmidt operator.
