On the behavior of the modulus of $m$-th derivatives of the algebraic polynomials in the whole complex plane without recurrence formula in the weighted Bergman space - Abdullayev, F. G.; Imashkyzy, M. (Ukrains’kyi Matematychnyi Zhurnal, 2026)
UDC 517.5We study the problem of growth of the $m$th derivatives of an arbitrary algebraic polynomial in weighted Bergman spaces in unbounded domains of the complex plane, without using the recurrence relation. We consider $k$-quasidisks and quasidisks with some additional functional conditions. These conditions enable us to combine several known classes of curves into a single class and obtain estimates for the growth of $m$th derivatives in this common class. By using similar estimates obtained for bounded quasidisks, we also provide estimates valid in the whole complex plane.