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In the unit disk of the complex plane, the Green functions for weighted biharmonic operators of the form Δω−1Δ are studied. The Green function is nonnegative everywhere if the weight function w is radial, logarithmically subharmonic, and area integrable. In the case of weighted Bergman classes, this fact allows us to establish the existence of a factorization of functions similar to the interior-exterior factorization in Hardy classes. Bibliography: 6 titles.

The green functions for weighted biharmonic operators of the form Δω−1Δ in the unit diskin the unit disk