Suppose that \(\Omega\) is a bounded planar domain with smooth boundary and let \(\Gamma_\Omega\) be the biharmonic Green function for \(\Omega\) with Dirichlet boundary conditions. It is known that if \(\Gamma_\Omega\) is positive throughout \(\Omega\times\Omega\), then \[ Q_\Omega(z,\zeta)\leq0,\qquad (z,\zeta)\in\partial\Omega\times \partial\Omega \setminus\Delta (\partial\Omega), \] where \(Q_\Omega\) is the harmonic Bergman kernel for \(\Omega\) and \(\Delta (\partial\Omega)=\{(z,z): z\in\partial\Omega\}\) is the boundary diagonal. The very interesting paper under review deals with the converse statement. Namely, the author proves that if \(\Omega\) is starshaped and the harmonic Bergman kernel is sufficiently negative on \(\partial\Omega\times\partial\Omega\setminus \Delta (\partial\Omega),\) then the biharmonic Green function is positive. A formula due to Hadamard is used which reduces the task to considering boundary value problems for \(\Delta^2u=0\) on a continuous family of subdomains of \(\Omega.\) This issue is treated by combining harmonic Bergman kernels with the theory of semigroups. Green functions for the weighted biharmonic operator \(\Delta \omega^{-1}\Delta \) are also considered in the unit disk \({\mathbb D}\) in the complex plane where \(\omega\colon\;{\mathbb D}\to (0,\infty)\) is a weight on \({\mathbb D}.\) Suitable conditions on \(\omega\) allow to derive estimates from below for the Green function.