Geodesic
$L_p$-convergence of~Bieberbach polynomials
Izvestiya. Mathematics , Tome 15 (1980) no. 2, pp. 349-371.

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The author proves the estimate $$ \|p_n-\omega\|_{L_p(G)}\leqslant\frac{c_{p,\varepsilon}}{(\ln\ln n)^{\frac18(1-\theta)-\varepsilon}} $$ where $G\subset\mathbf C$; $p_n(z)\equiv p_n$ are Bieberbach polynomials for the pair $(G,0)$; $\omega(0)=0$, $\omega'(0)=1$, $\omega(z)=\omega\colon G\to\{z;|z|$ is a conformal mapping, $\varepsilon>0$, $p\in[1,\infty)$, $0\theta\equiv\theta(G)$. The boundary $\partial G$ is more general than Lipschitz. Bibliography: 15 titles. 
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     title = {$L_p$-convergence {of~Bieberbach} polynomials},
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I. V. Kulikov. $L_p$-convergence of~Bieberbach polynomials. Izvestiya. Mathematics , Tome 15 (1980) no. 2, pp. 349-371. http://geodesic.mathdoc.fr/item/IM2_1980_15_2_a5/

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