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On the Growth of Derivatives of Algebraic Polynomials in Regions with Piecewise Smooth Boundary

by Cevahir D. Gün and Fahreddin G. Abdullayev

Posted: November 25, 2025
Server: Preprints.org
DOI: 10.20944/preprints202511.1944.v1

In this paper, we study the behavior of the m − th derivatives of general algebraic polynomials in weighted Bergman spaces defined in domains of the complex plane bounded by piecewise smooth curves with nonzero exterior angles and zero interior angles. Our approach involves establishing upper bounds on the growth of these derivatives not only interior of the unbounded domain but also on the closure of given domain. Through this analysis, we reveal detailed patterns in the growth of the m − th derivatives of algebraic polynomials throughout the complex plane, depending on the properties of the weighted function and the domain.

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