The Canonical Solution Operator to ∂ Restricted to Bergman Spaces
نویسنده
چکیده
Abstract. We first show that the canonical solution operator to ∂ 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 ∂ 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 Cn, n > 1, the corresponding operator fails to be a Hilbert-Schmidt operator. We also indicate a connection with the theory of Hankel operators.
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The Canonical Solution Operator to ∂ Restricted to Bergman Spaces and Spaces of Entire Functions
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