Mean oscillations and the convergence of Poisson integrals
We establish conditions for mean oscillations of a periodic summable function under which the summability of its Fourier series (conjugate series) by the Abel-Poisson method at a given point implies the convergence of Steklov means (the existence of the conjugate function) at the indicated point. Si...
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| Datum: | 1997 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4998 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511193738772480 |
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| author | Kolyada, V. I. Коляда, В. И. Коляда, В. И. |
| author_facet | Kolyada, V. I. Коляда, В. И. Коляда, В. И. |
| author_sort | Kolyada, V. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:31Z |
| description | We establish conditions for mean oscillations of a periodic summable function under which the summability of its Fourier series (conjugate series) by the Abel-Poisson method at a given point implies the convergence of Steklov means (the existence of the conjugate function) at the indicated point. Similar results are also obtained for the Poisson integral in ℝ+n+1. |
| first_indexed | 2026-03-24T03:09:00Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4998 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:09:00Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/aa/6109abc54cd181c2ba17ff50dc4eafaa.pdf |
| spelling | umjimathkievua-article-49982020-03-18T21:22:31Z Mean oscillations and the convergence of Poisson integrals Средние колебания и сходимость интегралов Пуассона Kolyada, V. I. Коляда, В. И. Коляда, В. И. We establish conditions for mean oscillations of a periodic summable function under which the summability of its Fourier series (conjugate series) by the Abel-Poisson method at a given point implies the convergence of Steklov means (the existence of the conjugate function) at the indicated point. Similar results are also obtained for the Poisson integral in ℝ+n+1. Знайдено умови на середні коливання періодичної сумовної функції, за яких із сумовності у точці методом Абеля - Пуассона її ряду Фур'є (спряженого ряду) випливає збіжність середніх Стєклова (існування спряженої функції) в цій точці. Аналогічні результати одержано для інтеграла Пуассона в ℝ+n+1. Institute of Mathematics, NAS of Ukraine 1997-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4998 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 2 (1997); 206–222 Український математичний журнал; Том 49 № 2 (1997); 206–222 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4998/6695 https://umj.imath.kiev.ua/index.php/umj/article/view/4998/6696 Copyright (c) 1997 Kolyada V. I. |
| spellingShingle | Kolyada, V. I. Коляда, В. И. Коляда, В. И. Mean oscillations and the convergence of Poisson integrals |
| title | Mean oscillations and the convergence of Poisson integrals |
| title_alt | Средние колебания и сходимость интегралов Пуассона |
| title_full | Mean oscillations and the convergence of Poisson integrals |
| title_fullStr | Mean oscillations and the convergence of Poisson integrals |
| title_full_unstemmed | Mean oscillations and the convergence of Poisson integrals |
| title_short | Mean oscillations and the convergence of Poisson integrals |
| title_sort | mean oscillations and the convergence of poisson integrals |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4998 |
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