Continuous pluriharmonic boundary values
Tom 91 / 2007
Annales Polonici Mathematici 91 (2007), 99-117
MSC: Primary 31C10; Secondary 32U15.
DOI: 10.4064/ap91-2-1
Streszczenie
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.
