On subextension of pluriharmonic and plurisubharmonic functions

Abstract

The problem of subextension of plurisubharmonic functions is considered. Recently it was shown by Cegrell–Zeriahi, that subextension is always possible for negative plurisubharmonic functions in the energy class ℱ. In this paper we construct, for every hyperconvex domain Ω, a negative plurisubharmonic function in the class ℰ which cannot be subextended. Given any pseudoconvex domain we construct a pluriharmonic function that cannot be subextended.