On the behavior of the modulus of m-th derivatives of algebraic polynomials in the whole complex plane without recurrence formula in the weighted Lebesgue space

ABDULLAYEV F., Imashkyzy M.

Filomat, vol.39, no.10, pp.3365-3379, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 10
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2510365a
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.3365-3379
  • Keywords: Algebraic polynomial, quasicircle, quasiconformal mapping
  • Uşak University Affiliated: Yes

Abstract

In this paper we study the growth of m − th derivatives of an arbitrary algebraic polynomial in weighted Lebesgue spaces in bounded and unbounded regions of the complex plane, ignoring the recurrence formula. We also provide estimates in the whole complex plane.