PUB - Publikationen an der Universität Bielefeld

Given a potentially bounded signed measure mu on a Brelot space (X, H) with Green function G, it is well known that mu-harmonic functions (i.e., in the classical case, finely continuous versions of solutions to Deltau- umu = 0) may be very discontinuous. In this paper it is shown that under very general assumptions on G ( satisfied for large classes of elliptic second-order linear differential operators) normalized perturbation, however, leads to a Brelot space (X, (H) over tilde (mu)) admitting a Green function T-mu(G) which is locally ( or even globally) comparable with G and has all properties required of G before. In particular, iterated perturbation is possible. Moreover, intrinsic Holder continuity of quotients of harmonic functions with respect to the local quasimetric rho:= (G(-1) + * G(-1))/ 2 yields rho-Holder continuity for quotients of mu-harmonic functions as well.