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5 Annales Polonici Mathematici

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Convergence in capacity

100%

Hiep P.

2008

tom 93

nr 1

91-99

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.

Boundary values of functions in Cegrell's class $𝓔_{ψ}$

100%

Hiep P.

nr 1

69-74

We study boundary values of functions in Cegrell's class $𝓔_{ψ}$.

The comparison principle and Dirichlet problem in the class $𝓔_p(f)$, p > 0

100%

Hiep P.

2006

tom 88

nr 3

247-261

We establish the comparison principle in the class $𝓔_p(f)$. The result obtained is applied to the Dirichlet problem in $𝓔_p(f)$.

Weighted Bernstein-Markov property in ℂⁿ

63%

Dieu N. , Hiep P.

2012

tom 105

nr 2

101-123

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.

ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

51%

Hai L. , Khue N. , Hiep P.

nr 1

25-41

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.