Boundary functions on a bounded balanced domain
Czechoslovak Mathematical Journal (2009)
- Volume: 59, Issue: 2, page 371-379
- ISSN: 0011-4642
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topKot, Piotr. "Boundary functions on a bounded balanced domain." Czechoslovak Mathematical Journal 59.2 (2009): 371-379. <http://eudml.org/doc/37929>.
@article{Kot2009,
abstract = {We solve the following Dirichlet problem on the bounded balanced domain $\Omega $ with some additional properties: For $p>0$ and a positive lower semi-continuous function $u$ on $\partial \Omega $ with $u(z)=u(\lambda z)$ for $|\lambda |=1$, $z\in \partial \Omega $ we construct a holomorphic function $f\in \mathbb \{O\}(\Omega )$ such that $u(z)=\int _\{\mathbb \{D\}z\}|f|^pd \mathfrak \{L\}_\{\mathbb \{D\}z\}^2$ for $z\in \partial \Omega $, where $\mathbb \{D\}=\lbrace \lambda \in \mathbb \{C\}\:|\lambda |<1\rbrace $.},
author = {Kot, Piotr},
journal = {Czechoslovak Mathematical Journal},
keywords = {boundary behavior of holomorphic functions; exceptional sets; boundary functions; Dirichlet problem; Radon inversion problem; boundary behavior; holomorphic function; exceptional set; boundary function; Dirichlet problem; Radon inversion problem},
language = {eng},
number = {2},
pages = {371-379},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundary functions on a bounded balanced domain},
url = {http://eudml.org/doc/37929},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Kot, Piotr
TI - Boundary functions on a bounded balanced domain
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 371
EP - 379
AB - We solve the following Dirichlet problem on the bounded balanced domain $\Omega $ with some additional properties: For $p>0$ and a positive lower semi-continuous function $u$ on $\partial \Omega $ with $u(z)=u(\lambda z)$ for $|\lambda |=1$, $z\in \partial \Omega $ we construct a holomorphic function $f\in \mathbb {O}(\Omega )$ such that $u(z)=\int _{\mathbb {D}z}|f|^pd \mathfrak {L}_{\mathbb {D}z}^2$ for $z\in \partial \Omega $, where $\mathbb {D}=\lbrace \lambda \in \mathbb {C}\:|\lambda |<1\rbrace $.
LA - eng
KW - boundary behavior of holomorphic functions; exceptional sets; boundary functions; Dirichlet problem; Radon inversion problem; boundary behavior; holomorphic function; exceptional set; boundary function; Dirichlet problem; Radon inversion problem
UR - http://eudml.org/doc/37929
ER -
References
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- Kot, P., 10.1090/S0002-9939-07-08939-3, Proc. Am. Math. Soc. 135 (2007), 3895-3903. (2007) Zbl1127.32005MR2341939DOI10.1090/S0002-9939-07-08939-3
- Kot, P., 10.1090/S0002-9939-08-09468-9, Proc. Amer. Math. Soc 137 (2009), 179-187. (2009) Zbl1157.32001MR2439439DOI10.1090/S0002-9939-08-09468-9
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