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 partial derivative-closed forms.