On the Behavior of Algebraic Polynomial in Unbounded Regions with Piecewise Dini-Smooth Boundary - Abdullayev, F. G.; Özkartepe, P. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
Let G ⊂ ℂ be a finite region bounded by a Jordan curve L := ∂G, let \( Ω :=ext\overline{G} \) (with respect to \( \overline{\mathbb{C}} \) ), let Δ := {w : |w| > 1}, and let w = Φ(z) be the univalent conformal mapping of Ω onto Δ normalized by Φ (∞) = ∞, Φ′(∞) > 0. Also let h(z) be a weight function and let A p (h,G), p > 0 denote a class of functions f analytic in G and satisfying the condition $$ {\left\Vert f\right\Vert}_{A_p\left(h,G\right)}^p:={\displaystyle \int {\displaystyle \underset{G}{\int }h(z){\left|f(z)\right|}^pdσ_z0 \) , for Jacobi-type weight function in regions with piecewise Dini-smooth boundary.