Journal d’Analyse Mathématique

, Volume 96, Issue 1, pp 283–295 | Cite as

On the maximum modulus principle for polynomials in a quasidisk

  • V. V. Andrievskii


LetG⊂C be a quasidisk,K ⊂ G be a compact set, andp n be a non-constant complex polynomial of degree at mostn. We establish the inequality\(\mathop {\max }\limits_{z \in K} |p_n (z)| \leqslant (1 - \alpha )\mathop {\max }\limits_{z \in \partial G} |p_n (z)|,\) whereα n < 0 depends onn, K,\(_{z \in \bar G} \left| {pn(z)} \right|\) and the geometrical structure of ϖG.


Jordan Curve Harmonic Measure Complex Polynomial Quasiconformal Extension Quasiconformal Homeomorphism 
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Copyright information

© The Hebrew University Magnes Press 2005

Authors and Affiliations

  • V. V. Andrievskii
    • 1
  1. 1.Department of Mathematical SciencesKent State UniversityKentUSA

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