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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| Дата: | 2026 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | 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| _version_ | 1860513283777232896 |
|---|---|
| author | Abdullayev, F. G. Imashkyzy, M. Аbdullayev, Fahreddin Abdullayev, F. G. Imashkyzy, M. |
| author_facet | Abdullayev, F. G. Imashkyzy, M. Аbdullayev, Fahreddin Abdullayev, F. G. Imashkyzy, M. |
| author_sort | Abdullayev, F. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T11:04:14Z |
| description | 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. |
| doi_str_mv | 10.3842/umzh.v78i1-2.8778 |
| first_indexed | 2026-03-24T03:42:13Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8778 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:42:13Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-87782026-03-21T11:04:14Z 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 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. Аbdullayev, Fahreddin Abdullayev, F. G. Imashkyzy, M. Bernstein-Markoff inequality, Walsh inequality, Algebraic polynomial, Quasiconformal mapping, Quasicircle, 30C30, 30E10, 30C70. 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. УДК 517.5 Про поведінку модуля $m$-х похідних алгебраїчних поліномів на всій комплексній площині без рекурентної формули у зваженому просторі Бергмана Розглянуто проблему зростання $m$-х похідних довільного алгебраїчного полінома у зважених просторах Бергмана в необмежених областях комплексної площини без урахування рекурентної формули. Розглянуто $k$-квазидиски та квазидиски з додатковими функціональними умовами. Ці умови дозволяють об'єднати кілька відомих класів кривих в один клас, для якого отримано оцінки зростання $m$-х похідних. З урахуванням подібних оцінок для обмежених квазидисків, отримано також оцінки, що справедливі на всій комплексній площині. Institute of Mathematics, NAS of Ukraine 2026-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8778 10.3842/umzh.v78i1-2.8778 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 1-2 (2026); 71–72 Український математичний журнал; Том 78 № 1-2 (2026); 71–72 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8778/10616 Copyright (c) 2026 F. G. Abdullayev, M. Imashkyzy |
| spellingShingle | Abdullayev, F. G. Imashkyzy, M. Аbdullayev, Fahreddin Abdullayev, F. G. Imashkyzy, M. 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 |
| title | 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 |
| title_alt | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic_facet | Bernstein-Markoff inequality Walsh inequality Algebraic polynomial Quasiconformal mapping Quasicircle, 30C30 30E10 30C70. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8778 |
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