On local properties of singular integral
UDC 517.5 Let $\gamma$ be a regular curve. We study the local properties of singular integrals in the $H_{\alpha }^{\alpha +\beta }(t_{0},\gamma)$ class of functions. We obtain a strengthening of the Plemelj\–Privalov theorem for functions from the class...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6959 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512561272717312 |
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| author | Mamedkhanov, J. I. Jafarov, S. Z. Mamedkhanov, J. I. Jafarov, S. Z. |
| author_facet | Mamedkhanov, J. I. Jafarov, S. Z. Mamedkhanov, J. I. Jafarov, S. Z. |
| author_sort | Mamedkhanov, J. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-06-13T15:56:14Z |
| description |
UDC 517.5
Let $\gamma$ be a regular curve. We study the local properties of singular integrals in the $H_{\alpha }^{\alpha +\beta }(t_{0},\gamma)$ class of functions. We obtain a strengthening of the Plemelj\–Privalov theorem for functions from the class $H_{\alpha }^{\alpha +\beta}(t_{0},\gamma).$ It is proved that, at the point $t_{0},$ of increased smoothness for $\alpha +\beta < 1,$ there is only a logarithmic loss. |
| doi_str_mv | 10.37863/umzh.v75i5.6959 |
| first_indexed | 2026-03-24T03:30:44Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6959 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:30:44Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-69592023-06-13T15:56:14Z On local properties of singular integral On local properties of singular integral Mamedkhanov, J. I. Jafarov, S. Z. Mamedkhanov, J. I. Jafarov, S. Z. Regular curve singular integral H\H local class of functios Plemelj-Privalov theorem UDC 517.5 Let $\gamma$ be a regular curve. We study the local properties of singular integrals in the $H_{\alpha }^{\alpha +\beta }(t_{0},\gamma)$ class of functions. We obtain a strengthening of the Plemelj\–Privalov theorem for functions from the class $H_{\alpha }^{\alpha +\beta}(t_{0},\gamma).$ It is proved that, at the point $t_{0},$ of increased smoothness for $\alpha +\beta < 1,$ there is only a logarithmic loss. УДК 517.5 Про локальні властивості сингулярного інтеграла Нехай $\gamma$ — регулярна крива. Досліджуються локальні властивості сингулярних інтегралів у класі функцій $H_{\alpha }^{\alpha +\beta }(t_{0},\gamma)$. Отримано посилення теореми Племеля–Привалова для функцій з класу $H_{\alpha }^{\alpha +\beta}(t_{0},\gamma).$ Доведено, що в точці $t_{0}$ підвищеної гладкості для $\alpha +\beta < 1$ є лише логарифмічні втрати. Institute of Mathematics, NAS of Ukraine 2023-05-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6959 10.37863/umzh.v75i5.6959 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 5 (2023); 614 - 627 Український математичний журнал; Том 75 № 5 (2023); 614 - 627 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6959/9771 Copyright (c) 2023 Sadulla Z Jafarov |
| spellingShingle | Mamedkhanov, J. I. Jafarov, S. Z. Mamedkhanov, J. I. Jafarov, S. Z. On local properties of singular integral |
| title | On local properties of singular integral |
| title_alt | On local properties of singular integral |
| title_full | On local properties of singular integral |
| title_fullStr | On local properties of singular integral |
| title_full_unstemmed | On local properties of singular integral |
| title_short | On local properties of singular integral |
| title_sort | on local properties of singular integral |
| topic_facet | Regular curve singular integral H\H local class of functios Plemelj-Privalov theorem |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6959 |
| work_keys_str_mv | AT mamedkhanovji onlocalpropertiesofsingularintegral AT jafarovsz onlocalpropertiesofsingularintegral AT mamedkhanovji onlocalpropertiesofsingularintegral AT jafarovsz onlocalpropertiesofsingularintegral |