On the growth of mth derivatives of algebraic polynomials in the weighted Lebesgue space

ABDULLAYEV F., Imashkyzy M.

Applied Mathematics in Science and Engineering, vol.30, no.1, pp.249-282, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1080/27690911.2022.2056170
  • Journal Name: Applied Mathematics in Science and Engineering
  • Journal Indexes: Scopus
  • Page Numbers: pp.249-282
  • Keywords: Algebraic polynomial, asymptotic conformal curve, quasiconformal mapping, quasismooth curve, smooth curve
  • Uşak University Affiliated: No

Abstract

In this paper, we study the growth of the mth derivative of an arbitrary algebraic polynomial in bounded and unbounded general domains of the complex plane in weighted Lebesgue spaces. Further, we obtain estimates for the derivatives at the closure of this regions. As a result, estimates for derivatives on the entire complex plane were found.