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 |
| Published: |
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| Summary: | 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. |
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| DOI: | 10.37863/umzh.v75i5.6959 |