Characterizations of plurisubharmonic functions

TL;DR

This paper provides new characterizations of (quasi-)plurisubharmonic functions using $L^p$-estimates of the $ar ext{d}$ operator and $L^p$-extensions of holomorphic functions, advancing understanding in complex analysis.

Contribution

It introduces novel characterizations of (quasi-)plurisubharmonic functions based on $L^p$-estimates and extensions, linking analytic properties to geometric function theory.

Findings

Characterizations of (quasi-)plurisubharmonic functions via $L^p$-estimates.

Development of criteria for $L^p$-extensions of holomorphic functions.

Enhanced understanding of the structure of plurisubharmonic functions.

Abstract

We give characterizations of (quasi-)plurisubharmonic functions in terms of $L^p$-estimates of $\bar\partial$ and $L^p$-extensions of holomorphic functions.