Higher Order Hulls in H∞, II

We give a complete characterization of the closed ideals in H∞ with hull contained in the set G of nontrivial Gleason parts and show that these ideals are uniquely determined by their higher order hulls. We apply our theorem to finitely generated ideals and obtain an extension of results of J. Bourgain. We also determine generating sets for the class of all ideals with hull contained in G.