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<p>We study the problem of growth of the <i>m</i>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 <i>k</i>-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 <i>m</i>th derivatives in this common class. By using similar estimates obtained for bounded quasidisks, we also provide estimates valid in the whole complex plane.</p>

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On the Behavior of the Modulus of mth Derivatives of the Algebraic Polynomials in the Whole Complex Plane Without Recurrence Formula in the Weighted Bergman Space

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • F. G. Abdullayev,
  • M. Imashkyzy

摘要

We study the problem of growth of the mth 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 mth derivatives in this common class. By using similar estimates obtained for bounded quasidisks, we also provide estimates valid in the whole complex plane.