Harmonic functions on finitely sheeted unlimited covering surfaces

We denote by HP(R) and (HB(R), resp.) the class of positive (bounded, resp.) harmonic functions on a Riemann surface R. Consider an open Riemann surface W possessing a Green's function and a p-sheeted (1 < p < infinity) unlimited covering surface W of W with projection map (p. We give a necessary and sufficient condition, in terms of Martin boundary, for HX(W) o phi = HX(W) (X = P, B). We also give some examples illustrating the above result when W is the unit disc.