Pluriharmonic extension in proper image domains
Volume 96 / 2009
Annales Polonici Mathematici 96 (2009), 163-174
MSC: Primary 31C10; Secondary 32U15.
DOI: 10.4064/ap96-2-4
Abstract
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 ${\mit\Omega}_\pi$ be the image of $D$ under the proper holomorphic map $\pi$. We characterize those continuous functions $f:\partial {\mit\Omega}_\pi\to\mathbb R$ that can be extended to a real-valued pluriharmonic function in ${\mit\Omega}_\pi$.
