Weighted pluricomplex energy
Abstract
Description
We study the complex Monge-Ampre operator on the classes of finite pluricomplex energy $\mathcal{E}_χ(Ω)$ in the general case ($χ(0)=0$ i.e. the total Monge-Ampre mass may be infinite). We establish an interpretation of these classes in terms of the speed of decrease of the capacity of sublevel sets and give a complete description of the range of the operator $(dd^c \cdot)^n$ on the classes $\mathcal{E}χ(Ω).$
Contrary to what we claimed in the previous version, in Theorem 5.1 we generalize some Theorem of Urban Cegrell but we do not give a new proof. To appear in Potenial Analysis
Contrary to what we claimed in the previous version, in Theorem 5.1 we generalize some Theorem of Urban Cegrell but we do not give a new proof. To appear in Potenial Analysis