Friedrich Haslinger
The canonical solution operator to d-bar restricted Bergman spaces.
Abstract.
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 the polydisc
and the unit ball in C^n, n>1, the
corresponding operator fails to be a Hilbert-Schmidt operator.
We also indicate a connection with the theory of Hankel operators.
friedrich.haslinger@univie.ac.at
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