The canonical solution operator to d-bar restricted to Bergman spaces
Complex Variables
2007-05-23 v1 Functional Analysis
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 polydisc and the unit ball in C^n, n>1, the corresponding operator fails to be a Hilbert-Schmidt operator.
Cite
@article{arxiv.math/0108035,
title = {The canonical solution operator to d-bar restricted to Bergman spaces},
author = {Friedrich Haslinger},
journal= {arXiv preprint arXiv:math/0108035},
year = {2007}
}
Comments
9 pages