Asymptotic Growth of Moduli of m-th Derivatives of Algebraic Polynomials in Weighted Bergman Spaces on Regions Without Zero Angles

In this paper, we study asymptotic bounds on the m-th derivatives of general algebraic polynomials in weighted Bergman spaces. We consider regions in the complex plane defined by bounded, piecewise, asymptotically conformal curves with strictly positive interior angles. We first establish asymptotic bounds on the growth in the exterior of a given unbounded region. We then extend our analysis to the closures of the region and derive the corresponding growth bounds. Combining these bounds with those for the corresponding exterior, we obtain comprehensive bounds on the growth of the m-th derivatives of arbitrary algebraic polynomials in the whole complex plane.