Pluriharmonic extension in proper image domains

Volume 96 / 2009

Rafa/l Czyż Annales Polonici Mathematici 96 (2009), 163-174 MSC: Primary 31C10; Secondary 32U15. DOI: 10.4064/ap96-2-4


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 ${\mit\Omega}_\pi$.


  • Rafa/l CzyżInstitute of Mathemathics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland

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