Uniform convergence of the generalized Bieberbach polynomials in regions with non-zero angles (Q1271957)

The Bieberbach polynomials \(P_n\) realize the minimum of a norm \(\| \phi_p-P_n\|_{L^1_p(G)}\) where \(\phi_p\) is an integral of \((\phi')^{2/p}\) and \(\phi\) is the conformal mapping of a finite complex domain \(G\) onto a disk. The author extends the uniform convergence of the Bieberbach polynomials to \(\phi_p(z)\) on \(\overline G\) and estimates the parameter \(\gamma\) of a bound \(\text{const.}/n^\gamma\) of the above norm. The approximation rate of the Bergman polynomials of \(G\) is also studied.