On the Growth of Derivatives of Algebraic Polynomials in Regions with a Piecewise Smooth Boundary

In this paper, we study the behavior of the m-th(m≥0) derivatives of general algebraic polynomials in weighted Bergman spaces defined in regions of the complex plane G bounded by piecewise smooth curves L=∂G with λπ(0<λ≤2) exterior angles relative to G. Upper bounds are found for the growth of the m-th derivatives of the polynomials not only inside the unbounded region but also on the closures of this region with both exterior non-zero angles λπ(0<λ<2) and interior zero angles (i.e., exterior angles 2π). The influence of the boundary angles λπ(0<λ≤2) of the region G and the “growth rate” of the weight function on the behavior of the moduli of polynomials and their derivatives in regions of the complex plane that are “symmetric” with respect to L (bounded and unbounded) is found.