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On the Dirichlet problem in the Cegrell classes

100%
Czyż R., Åhag P.
Annales Polonici Mathematici
|
2004
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tom 84
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nr 3
273-279
EN
Let μ be a non-negative measure with finite mass given by $φ(dd^{c}ψ)ⁿ$, where ψ is a bounded plurisubharmonic function with zero boundary values and $φ ∈ L^{q}((dd^{c}ψ)ⁿ)$, φ ≥ 0, 1 ≤ q ≤ ∞. The Dirichlet problem for the complex Monge-Ampère operator with the measure μ is studied.
2
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Continuous pluriharmonic boundary values

100%
Åhag P., Czyż R.
Annales Polonici Mathematici
|
2007
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tom 91
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nr 2-3
99-117
EN
Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D₁ × ⋯ × D_{s}$, j=1,...,s, s≥ 3. Also let 𝔾ₙ be the symmetrized polydisc in ℂⁿ, n ≥ 3. We characterize those real-valued continuous functions defined on the boundary of D or 𝔾ₙ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.
3
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Radially symmetric plurisubharmonic functions

81%
Åhag P., Czyż R., Persson L.
Annales Polonici Mathematici
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2012
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tom 106
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nr 1
1-17
EN
In this note we consider radially symmetric plurisubharmonic functions and the complex Monge-Ampère operator. We prove among other things a complete characterization of unitary invariant measures for which there exists a solution of the complex Monge-Ampère equation in the set of radially symmetric plurisubharmonic functions. Furthermore, we prove in contrast to the general case that the complex Monge-Ampère operator is continuous on the set of radially symmetric plurisubharmonic functions. Finally we characterize radially symmetric plurisubharmonic functions among the subharmonic ones using merely the laplacian.
4
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Concerning the energy class $𝓔_p$ for 0 < p < 1

81%
Åhag P., Czyż R., Hiêp P.
Annales Polonici Mathematici
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2007
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tom 91
|
nr 2-3
119-130
EN
The energy class $𝓔_{p}$ is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of $ℱ_{p}$ and its pluricomplex p-energy is proved.
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