Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions
UDC 517.5 We prove and discuss some new weak-type (1,1) inequalities for the maximal operators of  $T$ means with respect to the Vilenkin system generated by monotone coefficients.  We also apply these results to prove that  these $T$ means are&...
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| Дата: | 2023 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2023
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7163 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512619970953216 |
|---|---|
| author | Nadirashvili, N. Nadirashvili, N. |
| author_facet | Nadirashvili, N. Nadirashvili, N. |
| author_sort | Nadirashvili, N. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-08-15T15:57:32Z |
| description | UDC 517.5
We prove and discuss some new weak-type (1,1) inequalities for the maximal operators of  $T$ means with respect to the Vilenkin system generated by monotone coefficients.  We also apply these results to prove that  these $T$ means are  almost everywhere convergent. As applications, we present both some well-known and new results. |
| doi_str_mv | 10.37863/umzh.v75i7.7163 |
| first_indexed | 2026-03-24T03:31:40Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7163 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:40Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-71632023-08-15T15:57:32Z Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions Nadirashvili, N. Nadirashvili, N. Vilenkin groups, Vilenkin systems, partial sums of Vilenkin-Fourier series, $T$ means, Fejér mean, Riesz means, $L_{p}$ spaces, $weak-L_{p}$ spaces, maximal operator, inequalities. 42C10, 42B25. UDC 517.5 We prove and discuss some new weak-type (1,1) inequalities for the maximal operators of  $T$ means with respect to the Vilenkin system generated by monotone coefficients.  We also apply these results to prove that  these $T$ means are  almost everywhere convergent. As applications, we present both some well-known and new results. УДК 517.5 Збіжність $T$ середніх майже скрізь щодо системи інтегровних функцій Віленкіна  Доведено та обговорено деякі нові нерівності слабкого типу (1,1) для максимальних операторів  $T$ середніх щодо системи Віленкіна, породженої монотонними коефіцієнтами.  Отримані результати застосовано  для доведення того факту, що ці  $T$ середні збіжні майже скрізь. Як застосування наведено  деякі відомі та нові результати.  Institute of Mathematics, NAS of Ukraine 2023-07-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7163 10.37863/umzh.v75i7.7163 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 7 (2023); 933 - 945 Український математичний журнал; Том 75 № 7 (2023); 933 - 945 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7163/9754 Copyright (c) 2023 nato nadirashvili |
| spellingShingle | Nadirashvili, N. Nadirashvili, N. Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions |
| title | Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions |
| title_alt | Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions |
| title_full | Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions |
| title_fullStr | Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions |
| title_full_unstemmed | Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions |
| title_short | Almost everywhere convergence of $T$ means with respect to the Vilenkin system of integrable functions |
| title_sort | almost everywhere convergence of $t$ means with respect to the vilenkin system of integrable functions |
| topic_facet | Vilenkin groups Vilenkin systems partial sums of Vilenkin-Fourier series $T$ means Fejér mean Riesz means $L_{p}$ spaces $weak-L_{p}$ spaces maximal operator inequalities. 42C10 42B25. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7163 |
| work_keys_str_mv | AT nadirashvilin almosteverywhereconvergenceoftmeanswithrespecttothevilenkinsystemofintegrablefunctions AT nadirashvilin almosteverywhereconvergenceoftmeanswithrespecttothevilenkinsystemofintegrablefunctions |