Boundary functions in $L^{2}H\left({𝔹}^n\right)$

Kot, Piotr. "Boundary functions in $L^2H(\mathbb {B}^n)$." Czechoslovak Mathematical Journal 57.1 (2007): 29-47. <http://eudml.org/doc/31110>.

@article{Kot2007,
abstract = {We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball: For a function $u$ which is lower semi-continuous on $\partial \mathbb \{B\}^\{n\}$ we give necessary and sufficient conditions in order that there exists a holomorphic function $f\in \mathbb \{O\}(\mathbb \{B\}^\{n\})$ such that \[ u(z)=\int \_\{|\lambda |<1\}\left|f(\lambda z)\right|^\{2\}\mathrm \{d\}\{\mathfrak \{L\}\}^\{2\}(\lambda ). \]},
author = {Kot, Piotr},
journal = {Czechoslovak Mathematical Journal},
keywords = {boundary behavior of holomorphic functions; exceptional sets; boundary functions; computed tomography; Dirichlet problem; boundary behavior of holomorphic functions; exceptional sets; boundary functions; computed tomography; Dirichlet problem},
language = {eng},
number = {1},
pages = {29-47},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundary functions in $L^2H(\mathbb \{B\}^n)$},
url = {http://eudml.org/doc/31110},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Kot, Piotr
TI - Boundary functions in $L^2H(\mathbb {B}^n)$
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 29
EP - 47
AB - We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball: For a function $u$ which is lower semi-continuous on $\partial \mathbb {B}^{n}$ we give necessary and sufficient conditions in order that there exists a holomorphic function $f\in \mathbb {O}(\mathbb {B}^{n})$ such that \[ u(z)=\int _{|\lambda |<1}\left|f(\lambda z)\right|^{2}\mathrm {d}{\mathfrak {L}}^{2}(\lambda ). \]
LA - eng
KW - boundary behavior of holomorphic functions; exceptional sets; boundary functions; computed tomography; Dirichlet problem; boundary behavior of holomorphic functions; exceptional sets; boundary functions; computed tomography; Dirichlet problem
UR - http://eudml.org/doc/31110
ER -