An inequality for the beta function with application to pluripotential theory.
Plurisubharmonic extension in non-degenerate analytic polyhedra.
Continuous pluriharmonic boundary values
Let be a bounded hyperconvex domain in and set , 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
Let μ be a non-negative measure with finite mass given by , where ψ is a bounded plurisubharmonic function with zero boundary values and , φ ≥ 0, 1 ≤ q ≤ ∞. The Dirichlet problem for the complex Monge-Ampère operator with the measure μ is studied.
Radially symmetric plurisubharmonic functions
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 for 0 < p < 1
The energy class is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of and its pluricomplex p-energy is proved.
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