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Sums of continuous plurisubharmonic functions and the complex Monge- Ampère operator in \({\mathbb{C}}^ n\). (English) Zbl 0624.31004
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, E. Bedford and 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.
Reviewer: L.Gruman

MSC:
31C10 Pluriharmonic and plurisubharmonic functions
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References:
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