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
UDC 517.5 We 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. Th...
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| Datum: | 2026 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8778 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
We 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. |
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| DOI: | 10.3842/umzh.v78i1-2.8778 |