Geodesic
On estimates of the norm of the holomorphic component of a meromorphic function
Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 571-575 Cet article a éte moissonné depuis la source Math-Net.Ru

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For an arbitrary simply connected domain $D$, an estimate is obtained for the norm of the holomorphic component of a meromorphic function having a given number of poles in $D$. The estimate is uniform with respect to $D$. Bibliography: 4 titles. 
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A. A. Gonchar; L. D. Grigoryan. On estimates of the norm of the holomorphic component of a meromorphic function. Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 571-575. http://geodesic.mathdoc.fr/item/SM_1976_28_4_a9/

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[2] L. D. Grigoryan, “Otsenki normy golomorfnykh sostavlyayuschikh, meromorfnykh funktsii v oblastyakh s gladkoi granitsei”, Matem. sb., 100 (142) (1976), 156–164 | Zbl

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[4] T. Kövari, Ch. Pommerenke, “On Faber Polynomials and Faber Expansions”, Math. Z., 99 (1967), 193–206 | DOI | MR | Zbl