On the modulus of continuity of solid derivatives of a Cauchy-type integral
We establish sufficient conditions for the existence of solid derivatives of a continuous extension of a Cauchy-type integral onto the closure of a domain and obtain an estimate for the moduli of continuity of these derivatives. We prove that the Newton-Leibniz formula is true for certain classes of...
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| Datum: | 1998 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1998
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4917 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511099698282496 |
|---|---|
| author | Gerus, O. F. Герус, О. Ф. Герус, О. Ф. |
| author_facet | Gerus, O. F. Герус, О. Ф. Герус, О. Ф. |
| author_sort | Gerus, O. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:17:16Z |
| description | We establish sufficient conditions for the existence of solid derivatives of a continuous extension of a Cauchy-type integral onto the closure of a domain and obtain an estimate for the moduli of continuity of these derivatives. We prove that the Newton-Leibniz formula is true for certain classes of Jordan rectifiable curves. |
| first_indexed | 2026-03-24T03:07:31Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4917 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:07:31Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/3f/0a72b18c2278b03fee9f3c0920a7103f.pdf |
| spelling | umjimathkievua-article-49172020-03-18T21:17:16Z On the modulus of continuity of solid derivatives of a Cauchy-type integral О модуле непрерывности телесных производных интеграла типа Коши Gerus, O. F. Герус, О. Ф. Герус, О. Ф. We establish sufficient conditions for the existence of solid derivatives of a continuous extension of a Cauchy-type integral onto the closure of a domain and obtain an estimate for the moduli of continuity of these derivatives. We prove that the Newton-Leibniz formula is true for certain classes of Jordan rectifiable curves. Встановлено достатні умови існування тілесних похідних неперервного продовження інтеграла типу Коші на замикання області та отримано оцінку їх модулів неперервності. Доведено справедливість формули Ньютона-Лейбніца на деяких класах жорданових спрямлюваних кривих. Institute of Mathematics, NAS of Ukraine 1998-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4917 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 4 (1998); 476–484 Український математичний журнал; Том 50 № 4 (1998); 476–484 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4917/6533 https://umj.imath.kiev.ua/index.php/umj/article/view/4917/6534 Copyright (c) 1998 Gerus O. F. |
| spellingShingle | Gerus, O. F. Герус, О. Ф. Герус, О. Ф. On the modulus of continuity of solid derivatives of a Cauchy-type integral |
| title | On the modulus of continuity of solid derivatives of a Cauchy-type integral |
| title_alt | О модуле непрерывности телесных производных интеграла типа Коши |
| title_full | On the modulus of continuity of solid derivatives of a Cauchy-type integral |
| title_fullStr | On the modulus of continuity of solid derivatives of a Cauchy-type integral |
| title_full_unstemmed | On the modulus of continuity of solid derivatives of a Cauchy-type integral |
| title_short | On the modulus of continuity of solid derivatives of a Cauchy-type integral |
| title_sort | on the modulus of continuity of solid derivatives of a cauchy-type integral |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4917 |
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