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Vietnam Journal of Mathematics 37:2&3 (2009) 295-313 

Local T-pluripolarity and T-pluripolarity of a Subset and some Cegrell's Pluricomplex Energy Classes Associated to a Positive Closed Current

Le Mau Hai and Nguyen Thac Dung

Abstract.  In this paper we establish the equivalence between the locally T-pluripolarity and the T-pluripolarity of a subset E in a domain Ω ∈Cⁿ. At the same time, in the same way as Cegrell, we introduce notions of Cegrell's pluricomplex energy classes associated to a positive closed current T of dimension q≥1: E^T₀(Ω),F^T(Ω), E^T(Ω). We give several results on the convergence, some inequalities in classes of pluricomplex energy in this new setting.

2000 Mathematics Subject Classification: 32U05, 32U20, 32U40.

Keywords: Positive closed currents, plurisubharmonic functions, T-capacity, T-pluripolar, locally T-pluripolar, T-pluricomplex energy.

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Published by Springer since January 2013