COMPACTNESS ESTIMATE FOR THE 0-NEUMANN PROBLEM ON A Q-PSEUDOCONVEX DOMAIN IN A STEIN MANIFOLD

We consider a smoothly bounded q-pseudoconvex domain S2 in an n dimensional Stein manifold X and suppose that the boundary bS2 of S2 satisfies (q - P) property, which is the natural variant of the classical P property. Then, one prove the compactness estimate for the partial differential -Neumann operator Nr,s in the Sobolev k space. Applications to the boundary global regularity for the partial differential -Neumann operator Nr,s in the Sobolev k-space are given. Moreover, we prove the boundary global regularity of the partial differential -operator on S2.