Hypoellipticity of the $\bar\partial$-Neumann problem by means of subelliptic multipliers

Abstract

We prove local hypoellipticity of the complex Laplacian $\Box$ and of the Kohn Laplacian $\Box_b$ in a pseudoconvex boundary when, for a system of cut-off $\eta$, the gradient $\partial_b\eta$ and the Levi form $\partial_b\bar\partial_b\eta^2$ are subelliptic multipliers in the sense of Kohn.