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

ABDULLAYEV F., Imashkyzy M.

Applied Mathematics in Science and Engineering, cilt.30, sa.1, ss.249-282, 2022 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/27690911.2022.2056170
  • Dergi Adı: Applied Mathematics in Science and Engineering
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.249-282
  • Anahtar Kelimeler: Algebraic polynomial, asymptotic conformal curve, quasiconformal mapping, quasismooth curve, smooth curve
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.