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 >= 3 we show that g(O)(beta) is again a Green kernel of a Markov Feller process, for any power beta is an element of [1, d/(d -2)). In dimension d = 2, we show the same result for g(O)(beta), for any beta >= 1 and for kernels exp alpha g(O) exp(alpha g(O)) - 1, for alpha is an element of(0, 2 pi), when O is an open Greenian regular set whose complement contains a ball.