Lebesgue inequalities for poisson integrals
We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the spaceL p ,p≥1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric ofL p . We show that the es...
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| Date: | 2000 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2000
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4474 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510605241221120 |
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| author | Serdyuk, A. S. Stepanets, O. I. Сердюк, А. С. Степанец, А. И. Сердюк, А. С. Степанец, А. И. |
| author_facet | Serdyuk, A. S. Stepanets, O. I. Сердюк, А. С. Степанец, А. И. Сердюк, А. С. Степанец, А. И. |
| author_sort | Serdyuk, A. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:29:37Z |
| description | We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the spaceL p ,p≥1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric ofL p . We show that the estimates obtained are unimprovable on some important functional subsets. |
| first_indexed | 2026-03-24T02:59:39Z |
| format | Article |
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| id | umjimathkievua-article-4474 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:59:39Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5b/4ee735c733fe07863f4aaf8f5dfb125b.pdf |
| spelling | umjimathkievua-article-44742020-03-18T20:29:37Z Lebesgue inequalities for poisson integrals Неравенства Лебега для интегралов Пуассона Serdyuk, A. S. Stepanets, O. I. Сердюк, А. С. Степанец, А. И. Сердюк, А. С. Степанец, А. И. We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the spaceL p ,p≥1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric ofL p . We show that the estimates obtained are unimprovable on some important functional subsets. Одержано оцінки відхилень часткових сум Фур'є на множинах інтегралів Пуассона функцій з простору $L_p,\; р > 1$, що виражаються через значення найкращих наближень таких функцій тригонометричними многочленами в метриці $L_p$. Показано непокращуваність отриманих оцінок на деяких важливих функціональних підмножинах. Institute of Mathematics, NAS of Ukraine 2000-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4474 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 6 (2000); 798–808 Український математичний журнал; Том 52 № 6 (2000); 798–808 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4474/5652 https://umj.imath.kiev.ua/index.php/umj/article/view/4474/5653 Copyright (c) 2000 Serdyuk A. S.; Stepanets O. I. |
| spellingShingle | Serdyuk, A. S. Stepanets, O. I. Сердюк, А. С. Степанец, А. И. Сердюк, А. С. Степанец, А. И. Lebesgue inequalities for poisson integrals |
| title | Lebesgue inequalities for poisson integrals |
| title_alt | Неравенства Лебега для интегралов Пуассона |
| title_full | Lebesgue inequalities for poisson integrals |
| title_fullStr | Lebesgue inequalities for poisson integrals |
| title_full_unstemmed | Lebesgue inequalities for poisson integrals |
| title_short | Lebesgue inequalities for poisson integrals |
| title_sort | lebesgue inequalities for poisson integrals |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4474 |
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