Geodesic
Continuous pluriharmonic boundary values
Per Åhag1 ; Rafał Czyż2
1 Mid Sweden University SE-851 70 Sundsvall, Sweden
2 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
Annales Polonici Mathematici, Tome 91 (2007) no. 2-3, pp. 99-117.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $D_{j}$ be a bounded hyperconvex domain in $\mathbb{C}^{n_{j}}$ and set $D=D_{1}\times\cdots\times D_{s}$, $j=1,\ldots,s$, $s\geq 3$. Also let $\mathbb{G}_n$ be the symmetrized polydisc in $\mathbb{C}^{n}$, $n\geq 3$. We characterize those real-valued continuous functions defined on the boundary of $D$ or $\mathbb{G}_n$ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.
DOI : 10.4064/ap91-2-1
Keywords: bounded hyperconvex domain mathbb set times cdots times ldots geq mathbb symmetrized polydisc mathbb geq characterize those real valued continuous functions defined boundary mathbb which extended inside pluriharmonic function application complete characterization compliant functions obtained

Per Åhag 1 ; Rafał Czyż 2

1 Mid Sweden University SE-851 70 Sundsvall, Sweden
2 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland 
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Per Åhag; Rafał  Czyż. Continuous pluriharmonic boundary values. Annales Polonici Mathematici, Tome 91 (2007) no. 2-3, pp. 99-117. doi : 10.4064/ap91-2-1. http://geodesic.mathdoc.fr/articles/10.4064/ap91-2-1/

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