In this paper, we prove the existence of weak solutions of equations of complex Monge–Ampère type for arbitrary measures, in particular, measures carried by pluripolar sets. As an application of the obtained result, we show the existence of weak solutions of equations of complex Monge–Ampère type in the class [Formula: see text] if there exist locally subsolutions.
Let [Formula: see text] be a complex variety in a bounded domain [Formula: see text] in [Formula: see text]. We are interested in finding sufficient conditions on [Formula: see text] so that plurisubharmonic functions which are bounded from above on [Formula: see text] can be approximated from above by continuous functions on [Formula: see text] and plurisubharmonic on [Formula: see text] Next, we discuss the possibility to extend a given real valued continuous function on [Formula: see text] to a maximal plurisubharmonic on [Formula: see text] which is continuous up to the boundary.
Abstract. The aim of this paper is to establish the equivalence between the nonpluripolarity of a compact set in a complex space and the property (LB ∞ ) for the dual space of the space of germs of holomorphic functions on that compact set.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.