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

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 them- 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.