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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 4, pp 567–584 | Cite as

On the Cegrell Classes Associated to a Positive Closed Current

  • Mohamed ZawayEmail author
Article
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Abstract

The aim of this paper is to study the operator (ddc▪)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 ℂn. 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 (ddc▪)qT. Then the author proves that all functions that belong to these classes are CT-quasi-continuous and that the comparison principle is valid for them.

Keywords

Positive closed current Plurisubharmonic function Capacity Monge-Ampère Operator 

2000 MR Subject Classification

32U40 32U05 32U20 

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Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences Ad DwadimiShaqra UniversityAd-DwadimiSaudi Arabia
  2. 2.Department of Mathematics, Faculty of Science of GabesUniversity of GabesZrig, GabesTunisia

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