On the Behavior of Algebraic Polynomial in Unbounded Regions with Piecewise Dini-Smooth Boundary
Let G ⊂ ℂ be a finite region bounded by a Jordan curve L := ∂G, let \( \Omega :=\mathrm{e}\mathrm{x}\mathrm{t}\overline{G} \) (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′(...
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| Datum: | 2014 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2014
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2161 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Let G ⊂ ℂ be a finite region bounded by a Jordan curve L := ∂G, let \( \Omega :=\mathrm{e}\mathrm{x}\mathrm{t}\overline{G} \) (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|}^pd{\sigma}_z0 \) , for Jacobi-type weight function in regions with piecewise Dini-smooth boundary. |
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