Subnormal tuples on strictly pseudoconvex and bounded symmetric domains

Multivariable extensions of the Scott Brown technique are used to prove that on a quite general class of domains D in C-n, or in a complex submanifold of C-n, each subnormal tuple T is an element of L(H)(n) with an isometric weak* continuous H-infinity(D)-functional calculus is reflexive. To obtain our results we use methods developed by Aleksandrov in his abstract approach to the inner function problem, and we prove new results for Henkin measures on suitable complex domains.