ON THE UNIFORM CONVERGENCE OF THE GENERALIZED BIEBERBACH POLYNOMIALS IN REGIONS WITH K-QUASICONFORMAL BOUNDARY

摘要

Let G be a finite domain in the complex plane with K-quasicon formal boundary, zo be an arbitrary fixed point in G and p>0. Letρ(z) be the conformal mapping from G onto the disk with radius r_o>0 and centered at the origin 0, normalized by ρ(z_0)=0 and ρ(z_o)=1. Let us set ρ_p(z)∫~z_zo[ρ(ζ)]~2/pdζ, and let π_n.p(z) be.