An application of fine potential theory to prove a Phragmen Lindelöf theorem
Annales de l'Institut Fourier, Volume 34 (1984) no. 2, p. 63-66

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{|z|>r} for some positive r and f has a simple pole.

On donne une nouvelle démonstration d’un théorème de W.H.J. Fuchs du type Phragmén Lindelöf pour les ouverts U quelconques du plan ouvert : soit f holomorphe dans U et bornée aux environs de la frontière de U croissante ou plus comme un polynôme; alors ou f est bornée ou f a un pôle simple à l’infini.

@article{AIF_1984__34_2_63_0,
     author = {Lyons, Terry J.},
     title = {An application of fine potential theory to prove a Phragmen Lindel\"of theorem},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {34},
     number = {2},
     year = {1984},
     pages = {63-66},
     doi = {10.5802/aif.964},
     zbl = {0522.30024},
     mrnumber = {86c:30042},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1984__34_2_63_0}
}
Lyons, Terry J. An application of fine potential theory to prove a Phragmen Lindelöf theorem. Annales de l'Institut Fourier, Volume 34 (1984) no. 2, pp. 63-66. doi : 10.5802/aif.964. http://www.numdam.org/item/AIF_1984__34_2_63_0/

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