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

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.

Keywords

• algebraic polynomial
• quasiconformal mapping
• smooth curve
• quasismooth curve
• asymptotic conformal curve