  In this article we study stability properties of $g_O$, the standard Green
kernel for $O$ an open regular set in $R^d$. In $d\ge 3$ we show that
$g_O^\beta$ is again a Green kernel of a Markov Feller process, for any power
$\beta\in [1,d/(d-2))$. In dimension $d=2$, if $O$ is an open Greenian regular
set, we show the same result for $g_O^\beta$, for any $\beta\ge 1$ and for the
kernel $\exp(\alpha g_O)$, when $\alpha \in (0,2\pi)$.
