An application of fine potential theory to prove a Phragmen Lindelöf theorem

Lyons, Terry J.. "An application of fine potential theory to prove a Phragmen Lindelöf theorem." Annales de l'institut Fourier 34.2 (1984): 63-66. <http://eudml.org/doc/74636>.

@article{Lyons1984,
abstract = {We give a new proof of a Phragmén Lindelöf theorem due to W.H.J. Fuchs and valid for an arbitrary open subset $U$ of the complex plane: if $f$ is analytic on $U$, bounded near the boundary of $U$, and the growth of $j$ is at most polynomial then either $f$ is bounded or $U\supset \lbrace |z| &gt;r\rbrace $ for some positive $r$ and $f$ has a simple pole.},
author = {Lyons, Terry J.},
journal = {Annales de l'institut Fourier},
keywords = {Phragmen-Lindelöf theorem},
language = {eng},
number = {2},
pages = {63-66},
publisher = {Association des Annales de l'Institut Fourier},
title = {An application of fine potential theory to prove a Phragmen Lindelöf theorem},
url = {http://eudml.org/doc/74636},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Lyons, Terry J.
TI - An application of fine potential theory to prove a Phragmen Lindelöf theorem
JO - Annales de l'institut Fourier
PY - 1984
PB - Association des Annales de l'Institut Fourier
VL - 34
IS - 2
SP - 63
EP - 66
AB - We give a new proof of a Phragmén Lindelöf theorem due to W.H.J. Fuchs and valid for an arbitrary open subset $U$ of the complex plane: if $f$ is analytic on $U$, bounded near the boundary of $U$, and the growth of $j$ is at most polynomial then either $f$ is bounded or $U\supset \lbrace |z| &gt;r\rbrace $ for some positive $r$ and $f$ has a simple pole.
LA - eng
KW - Phragmen-Lindelöf theorem
UR - http://eudml.org/doc/74636
ER -