On the behavior of m-th derivatives of polynomials in bounded and unbounded regions without zero angles in weighted Lebesgue spaces

Abdullayev F., Imashkyzy M.

Analysis and Mathematical Physics, cilt.15, sa.3, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 3
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s13324-025-01055-9
  • Dergi Adı: Analysis and Mathematical Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Algebraic polynomial, Asymptotically conformal curves, Bernstein-Markoff inequality, Quasicircle, Quasiconformal mapping, Walsh inequality
  • Uşak Üniversitesi Adresli: Evet

Özet

In this paper, we study the growth of the m-th (m≥1) derivatives of an arbitrary algebraic polynomial in weighted Lebesgue spaces over the whole complex plane. We first study the growth of the m-th derivatives of an arbitrary algebraic polynomial over unbounded regions of the complex plane, and then we obtain estimates for the growth of the m-th derivatives of this polynomial over the closure of the given region. Combining both estimates, we find estimates for the growth of the m-th derivatives of an arbitrary algebraic polynomial over the whole complex plane.