Plurisubharmonic functions with weak singularities

Details Plurisubharmonic functions with weak singularities Plurisubharmonic functions with weak singularities

2008-02-22

arxiv.org/abs/0802.3265v1

Mathematics

Complex Variables

15 pages, dedicated to Christer Kiselman on the occasion of his retirement

Scientific paper

We study the complex Monge-Amp\`ere operator in bounded hyperconvex domains of $\C^n$. We introduce a scale of classes of weakly singular plurisubharmonic functions : these are functions of finite weighted Monge-Amp\`ere energy. They generalize the classes introduced by U.Cegrell, and give a stratification of the space of (almost) all unbounded plurisubharmonic functions. We give an interpretation of these classes in terms of the speed of decreasing of the Monge-Amp\`ere capacity of sublevel sets and solve associated complex Monge-Amp\`ere equations.

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