Sums of continuous plurisubharmonic functions and the complex Monge- Ampère operator in \({\mathbb{C}}^ n\)
In pluricomplex analysis of n variables, the nonlinear complex Monge- Ampère equation \((dd^ c)^ n\) plays the same role as the Laplacian operator for one complex variable. Unfortunately, for V an arbitrary plurisubharmonic function, it is not always possible to define \((dd^ cV)^ n\). In their now classical work, \textit{E. Bedford} and \textit{B. A. Taylor} [Acta Math. 149, 1-40 (1982; Zbl 0547.32012)] showed that one can define \((dd^ cV)^ n\) for V locally bounded. The author shows that one can define \((dd^ cV)^ n\) for all \(V=\sum^{\infty}_{j=1}V_ j\) for \(V_ j\) continuous negative plurisubharmonic functions such that the sums \((dd^ c \sum^{N}_{j=1}V_ j)\) is uniformly bounded on complex subsets of D independently of N. He also studies convergence properties for the Monge-Ampère equation in this class of plurisubharmonic functions.
scientific article; zbMATH DE number 4013010