A von Neumann type inequality for certain domains in C-n

Strict contractions on a Hilbert space have a functional calculus with functions that are analytic in the unit disc of the complex plane; an estimate of the norm is then provided by von Neumann's inequality. We consider functions that satisfy related inequalities with respect to multioperators connected to certain domains in C-n; a representation formula and a Nevanlinna-Pick type theorem are obtained.