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1
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A characterization of bounded plurisubharmonic functions

100%
Hiep P.
Annales Polonici Mathematici
|
2005
|
tom 85
|
nr 3
233-238
EN
We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.
2
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Convergence in capacity

100%
Hiep P.
Annales Polonici Mathematici
|
2008
|
tom 93
|
nr 1
91-99
EN
We prove that if $𝓔(Ω) ∋ u_j → u ∈ 𝓔(Ω)$ in Cₙ-capacity then $lim inf_{j→ ∞}(dd^cu_j)^{n} ≥ 1_{u>-∞}(dd^cu)^{n}$. This result is used to consider the convergence in capacity on bounded hyperconvex domains and compact Kähler manifolds.
3
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Boundary values of functions in Cegrell's class $𝓔_{ψ}$

100%
Hiep P.
Annales Polonici Mathematici
|
2007
|
tom 92
|
nr 1
69-74
EN
We study boundary values of functions in Cegrell's class $𝓔_{ψ}$.
4
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The comparison principle and Dirichlet problem in the class $𝓔_p(f)$, p > 0

100%
Hiep P.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 3
247-261
EN
We establish the comparison principle in the class $𝓔_p(f)$. The result obtained is applied to the Dirichlet problem in $𝓔_p(f)$.
5
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Weighted Bernstein-Markov property in ℂⁿ

64%
Dieu N., Hiep P.
Annales Polonici Mathematici
|
2012
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tom 105
|
nr 2
101-123
EN
We study the weighted Bernstein-Markov property for subsets in ℂⁿ which might not be bounded. An application concerning approximation of the weighted Green function using Bergman kernels is also given.
6
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ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

51%
Hai L., Khue N., Hiep P.
Annales Polonici Mathematici
|
2007
|
tom 91
|
nr 1
25-41
EN
We establish some results on ω-pluripolarity and complete ω-pluripolarity for sets in a compact Kähler manifold X with fundamental form ω. Moreover, we study subextension of ω-psh functions on a hyperconvex domain in X and prove a comparison principle for the class 𝓔(X,ω) recently introduced and investigated by Guedj-Zeriahi.
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