It is shown that if denotes a harmonic morphism of type Bl between suitable Brelot harmonic spaces and , then a function , defined on an open set , is superharmonic if and only if is superharmonic on . The “only if” part is due to Constantinescu and Cornea, with denoting any harmonic morphism between two Brelot spaces. A similar result is obtained for finely superharmonic functions defined on finely open sets. These results apply, for example, to the case where is the projection from to () or where is the radial projection from to the unit sphere in ().
"Harmonic morphisms applied to classical potential theory." Nagoya Math. J. 202 107 - 126, June 2011. https://doi.org/10.1215/00277630-1260468