Hypoellipticity of the Kohn-Laplacian $$\Box _b$$ □ b and 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 $$\frac{1}{2}(\partial _b\bar{\partial }_b-\bar{\partial }_b\partial _b)\eta $$ are subelliptic multipliers in the sense of Kohn (Acta Math 142:79–122, 1979).