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.
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
Affiliations des auteurs :
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
@article{10_4064_ap91_2_1,
author = {Per \r{A}hag and Rafa{\l} Czy\.z},
title = {Continuous pluriharmonic boundary values},
journal = {Annales Polonici Mathematici},
pages = {99--117},
year = {2007},
volume = {91},
number = {2-3},
doi = {10.4064/ap91-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap91-2-1/}
}
TY - JOUR
AU - Per Åhag
AU - Rafał Czyż
TI - Continuous pluriharmonic boundary values
JO - Annales Polonici Mathematici
PY - 2007
SP - 99
EP - 117
VL - 91
IS - 2-3
UR - http://geodesic.mathdoc.fr/articles/10.4064/ap91-2-1/
DO - 10.4064/ap91-2-1
LA - en
ID - 10_4064_ap91_2_1
ER -
