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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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