In this paper we study the Cauchy–Riemann equation in complex projective spaces. Specifically, we use the modified weight function method to study the ∂̄-Neumann problem on pseudoconvex domains in these spaces. The solutions are used to study function theory on pseudoconvex domains via the ∂̄-Cauchy problem. We apply our results to prove nonexistence of Lipschitz Levi-flat hypersurfaces in comple...
