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Continuous pluriharmonic boundary values

Per Åhag; Rafał Czyż — 2007

Annales Polonici Mathematici

Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D ₁ \times \dots \times D_{s}$ , j=1,...,s, s≥ 3. Also let ₙ be the symmetrized polydisc in ℂⁿ, n ≥ 3. We characterize those real-valued continuous functions defined on the boundary of D or ₙ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.

On the Dirichlet problem in the Cegrell classes

Rafał Czyż; Per Åhag — 2004

Annales Polonici Mathematici

Let μ be a non-negative measure with finite mass given by $φ (d d^{c} ψ) ⁿ$ , where ψ is a bounded plurisubharmonic function with zero boundary values and $φ \in L^{q} ((d d^{c} ψ) ⁿ)$ , φ ≥ 0, 1 ≤ q ≤ ∞. The Dirichlet problem for the complex Monge-Ampère operator with the measure μ is studied.

Radially symmetric plurisubharmonic functions

Per Åhag; Rafał Czyż; Leif Persson — 2012

Annales Polonici Mathematici

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...

Concerning the energy class $_{p}$ for 0 < p < 1

Per Åhag; Rafał Czyż; Pham Hoàng Hiêp — 2007

Annales Polonici Mathematici

The energy class $_{p}$ 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.