A transformation rule associated with P - extremal functions and holomorphic mappings

Klimek (In: Pluripotential theory, The Clarendon Press Oxford University Press, New York, 1991) proved a transformation rule for standard extremal functions V-K in pluripotential theory subject to holomorphic mappings f, under certain conditions on f. Here, by considering the P- extremal functions V-P,V-K for two different convex bodies P, we present a similar result that we have discovered in the setting of P- pluripotential theory. Three types of candidates that satisfy the hypotheses will also be illustrated. This result is particularly applicable in determining V(P,K )for some non product sets K.