The Donnelly-Fefferman theorem on $q$-pseudoconvex domains

Abstract

In this paper we introduce a notion of $q$-subharmonicity for non-smooth functions and then using $q$-subharmonic exhaustion function, define a $q$-pseudoconvexity which is applicable to the domain with non-smooth boundary. Among others, we generalize the Donnelly-Fefferamn type theorem on $q$-pseudoconvex domains and as an application of this theorem, we give approximation theorem for $\overline{\partial}$-closed forms.