Geodesic
Cauchy's integral formula in domains of arbitrary connectivity
Sbornik. Mathematics, Tome 191 (2000) no. 8, pp. 1215-1231

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that a straightforward generalization of Cauchy's integral formula is possible only in domains with boundary of finite length (in some sense or other). An example of a simply connected domain with boundary of infinite length is constructed such that for fairly general functionals on $H^\infty$ no extremal function (including the Ahlfors function) can be represented as a Cauchy potential. 
@article{SM_2000_191_8_a4,
     author = {M. V. Samokhin},
     title = {Cauchy's integral formula in domains of arbitrary connectivity},
     journal = {Sbornik. Mathematics},
     pages = {1215--1231},
     publisher = {mathdoc},
     volume = {191},
     number = {8},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_8_a4/}
}
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M. V. Samokhin. Cauchy's integral formula in domains of arbitrary connectivity. Sbornik. Mathematics, Tome 191 (2000) no. 8, pp. 1215-1231. http://geodesic.mathdoc.fr/item/SM_2000_191_8_a4/