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Vietnam
Journal of Mathematics 37:2&3 (2009) 295-313
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Local T-pluripolarity and T-pluripolarity
of a Subset and some Cegrell's Pluricomplex Energy Classes Associated to a
Positive Closed Current
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Le Mau Hai and
Nguyen Thac Dung
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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:
ET0(Ω),FT(Ω), ET(Ω).
We give several results on the convergence, some inequalities in classes of
pluricomplex energy in this new setting.
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2000 Mathematics Subject Classification: 32U05, 32U20,
32U40.
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Keywords: Positive closed currents,
plurisubharmonic functions, T-capacity, T-pluripolar, locally
T-pluripolar, T-pluricomplex energy.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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