Geodesic
Estimates of the norm of the holomorphic components of functions meromorphic in domains with a smooth boundary
Sbornik. Mathematics, Tome 29 (1976) no. 1, pp. 139-146 
L. D. Grigoryan. Estimates of the norm of the holomorphic components of functions meromorphic in domains with a smooth boundary. Sbornik. Mathematics, Tome 29 (1976) no. 1, pp. 139-146. http://geodesic.mathdoc.fr/item/SM_1976_29_1_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $D$ be a Jordan domain with smooth boundary, $f$ a function meromorphic in $D$, and $f^*$ the holomorphic component of $f$ in $D$. It is shown that $\|f^*\|_{\partial D}\leqslant C(D)n\|f\|_{\partial D}$, where $n$ is the number of poles of $f$ in $D$. Bibliography: 8 titles.

[1] A. A. Gonchar, L. D. Grigoryan, “Ob otsenkakh normy golomorfnoi sostavlyayuschei meromorfnoi funktsii”, Matem. sb., 99(141):4 (1976), 634–638 | MR | Zbl

[2] V. E. Katsnelson, “O nekotorykh operatorakh, deistvuyuschikh v prostranstvakh, porozhdennykh funktsiyami $\frac1{t-z_k}$”, Teoriya funktsii, funkts. analiz i ikh prilozheniya, no. 4, Kharkov, 1967, 58–66

[3] A. M. Bochtein, V. E. Katsnelson, “Ob otsenke normy proektora v odnom prostranstve analiticheskikh funktsii”, Teoriya funktsii, funkts. analiz i ikh prilozheniya, no. 12, Kharkov, 1970, 81–85

[4] G. Polia, G. Sege, Izoperimetricheskie neravenstva v matematicheskoi fizike, Fizmatgiz, Moskva, 1962 | MR

[5] A. A. Gonchar, “O zadachakh E. I. Zolotareva, svyazannykh s ratsionalnymi funktsiyami”, Matem. sb., 78 (120) (1969), 640–654 | Zbl

[6] A. A. Gonchar, “Skorost ratsionalnoi approksimatsii i svoistvo odnoznachnosti analiticheskoi funktsii v okrestnosti izolirovannoi osoboi tochki”, Matem. sb., 94(136) (1974), 265–282 | Zbl

[7] D. J. Newman, “Rational approximation to $|x|$”, Michigan Math. J., 11 (1964), 11–14 | DOI | MR | Zbl

[8] A. A. Gonchar, “O nailuchshikh priblizheniyakh ratsionalnymi funktsiyami”, DAN SSSR, 100:2 (1955), 205–208 | Zbl