Abstract
Compactness of the (partial derivative) over bar -Neumann operator N-s on uniformly q-convex intersection in C-n is established. In fact, we prove the significantly stronger fact that the (partial derivative) over bar -Neumann operator satisfies a subelliptic gain of one half derivative in the L-2-Sobolev spaces, so that compactness of N-s follows immediately from Rellich's lemma. Applications for the Fredholm theory of Toeplitz operators are also provided.