Estimates for the p-Green function near the pole

We study the asymptotic expansion of p-Green functions and their derivatives near the pole.

In the Euclidean setting, we strengthen a theorem from [arXiv:2203.01206] by establishing improved integrability properties and estimates for the first and second derivatives.

In the more general Riemannian setting, we derive a refined asymptotic expansion of the p-Green function near its pole, thereby improving the corresponding result proved in [arXiv:2512.14591].