Construction of Green functions for weighted biharmonic operators

A constructive proof is given of the existence of the weighted biharmonic Green function Γα for α 0. The method is used to derive the explicit formula for Γ1 previously stated by Hedenmalm. In addition, a formula for Γ2 is found, which is then shown to take both positive and negative values in the bidisk D ×D.  2003 Elsevier Inc. All rights reserved.