A mean value criterion for plurisubharmonic functions

TL;DR

This paper introduces a new criterion based on integral means over complex ellipsoids to characterize plurisubharmonic functions and extends classical theorems to this setting.

Contribution

It provides a novel mean value criterion for plurisubharmonic functions and establishes an analogue of the Blaschke-Privalov theorem for them.

Findings

Established a mean value criterion for plurisubharmonic functions.

Proved an analogue of the Blaschke-Privalov theorem in this context.

Abstract

In this paper we prove a criterion for plurisubharmonic functions in terms of integral mean by complex ellipsoids. Moreover, by using the criterion we prove an analogue of Blaschke-Privalov theorem for plurisubharmonic functions.