Continuous pluriharmonic boundary values

Volume 91 / 2007

Per Åhag, Rafał Czyż Annales Polonici Mathematici 91 (2007), 99-117 MSC: Primary 31C10; Secondary 32U15. DOI: 10.4064/ap91-2-1

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 $\mathbb{G}_n$ 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.

Authors

  • Per ÅhagMid Sweden University
    SE-851 70 Sundsvall, Sweden
    e-mail
  • Rafał CzyżInstitute of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Kraków, Poland
    e-mail

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