On the Cegrell Classes Associated to a Positive Closed Current

Mohamed Zaway

Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (4) : 567 -584.

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Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (4) : 567 -584. DOI: 10.1007/s11401-019-0152-6
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On the Cegrell Classes Associated to a Positive Closed Current

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Abstract

The aim of this paper is to study the operator (dd c▪) qT on some classes of plurisubharmonic (psh) functions, which are not necessary bounded, where T is a positive closed current of bidimension (q, q) on an open set Ω of ℂ n. The author introduces two classes ${\cal F}_p^T\left( {\rm{\Omega }} \right)$ and ${\cal E}_p^T\left( {\rm{\Omega }} \right)$ and shows first that they belong to the domain of definition of the operator (dd c▪) qT. Then the author proves that all functions that belong to these classes are C T-quasi-continuous and that the comparison principle is valid for them.

Keywords

Positive closed current / Plurisubharmonic function / Capacity / Monge-Ampère Operator

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Mohamed Zaway. On the Cegrell Classes Associated to a Positive Closed Current. Chinese Annals of Mathematics, Series B, 2019, 40(4): 567-584 DOI:10.1007/s11401-019-0152-6

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