ON THE TRACE INEQUALITIES FOR HARDY-SOBOLEV FUNCTIONS IN THE UNIT BALL OF C-N

We characterize ''invariant measures'' on the spheres in C-n for which the trace inequality, integral s(M(alpha)F)(p) d mu less than or equa l to C parallel to F parallel to(Hp beta),(p) holds for holomorphic fu nctions F in the Hardy-Sobolev spaces H-beta(p) where 1 < p < infinity , and M(alpha) is the admissible maximal function. In contrast to the known imbedding theorems for Euclidean Sobolev spaces, we obtain chara cterizations that distinguish the cases 1 < p less than or equal to 2 and 2 < p < infinity. Applications to exceptional sets are also given.