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 Cet article a éte moissonné depuis la source Math-Net.Ru

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

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