On the Green function for the weighted biharmonic operator \(\Delta w^{-1}\Delta\) in the unite disk (Q2714018)

The aim of the article is to prove positivity of the Green function for the weighted biharmonic operator \(\Delta w^{-1}\Delta\) in the unit disk \(\mathbb D\) in the case when the weighted function \(w\) is an arbitrary radial and logarithmic subharmonic positive function (summable) on \(\mathbb D\). The result obtained makes it possible to bring into consideration the Bergmann class of functions that possesses the so-called factorization property. This property is the well-known analog of the internally-exterior factorization for the Hardy classes.