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

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

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. 
@article{IM2_1980_15_2_a5,
     author = {I. V. Kulikov},
     title = {$L_p$-convergence {of~Bieberbach} polynomials},
     journal = {Izvestiya. Mathematics },
     pages = {349--371},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1980_15_2_a5/}
}
TY  - JOUR
AU  - I. V. Kulikov
TI  - $L_p$-convergence of~Bieberbach polynomials
JO  - Izvestiya. Mathematics 
PY  - 1980
SP  - 349
EP  - 371
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1980_15_2_a5/
LA  - en
ID  - IM2_1980_15_2_a5
ER  - 
%0 Journal Article
%A I. V. Kulikov
%T $L_p$-convergence of~Bieberbach polynomials
%J Izvestiya. Mathematics 
%D 1980
%P 349-371
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1980_15_2_a5/
%G en
%F IM2_1980_15_2_a5
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/