Growth Estimates for m-th (m ≥ 1) Derivatives of Algebraic Polynomials in Domains with Piecewise Quasismooth Boundaries

In this paper, we investigate the growth behavior of the m-th derivatives (m≥1) of arbitrary algebraic polynomials in bounded and unbounded domains whose boundaries are piecewise quasismooth curve and possess interior and exterior zero angles of power type, within weighted Lebesgue spaces. We derive estimates for the growth of these derivatives in terms of the characteristics of the weight function, the geometric properties of the boundary, and the tangency exponents of the boundary arcs at their junction points. The obtained estimates are established both in the closure of the bounded domain and at exterior points, while the pointwise estimates in the unbounded domain additionally reflect the location of the point within the domain.