Estimates for the -Neumann problem and nonexistence of C2 Levi-flat hypersurfaces in

Abstract

Letbe a pseudoconvex domain with C 2 boundary in CP n , n ≥ 2. We prove that the ¯ ∂-Neumann operator N exists for square-integrable forms on � . Furthermore, there exists a number � 0 > 0 such that the operators N , ¯ ∂ ∗ N , ¯ ∂N and the Bergman projection are regular in the Sobolev space W � (�) for � 0 and n ≥ 2. As a consequence, we prove the nonexistence of C 2 Levi-flat hypersurfaces in CP n .