ON \(\Lambda\)-CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIES
We consider one type of convergence of multiple trigonometric Fourier series intermediate between the convergence over cubes and the \(\lambda \)-convergence for \(\lambda >1\). The well-known result on the almost everywhere convergence over cubes of Fourier series of functions from the class \(...
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2017-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/99 |
| _version_ | 1811313104453107712 |
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| author | Nikolai Yu. Antonov |
| author_facet | Nikolai Yu. Antonov |
| author_sort | Nikolai Yu. Antonov |
| collection | DOAJ |
| description | We consider one type of convergence of multiple trigonometric Fourier series intermediate between the convergence over cubes and the \(\lambda \)-convergence for \(\lambda >1\). The well-known result on the almost everywhere convergence over cubes of Fourier series of functions from the class \( L (\ln ^ + L) ^ d \ln ^ + \ln ^ + \ln ^ + L ([0,2 \pi)^d ) \) has been generalized to the case of the \( \Lambda \)-convergence for some sequences \(\Lambda\). |
| first_indexed | 2024-04-13T10:49:30Z |
| format | Article |
| id | doaj.art-b25f1a66236641008561affd96ebeab3 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-04-13T10:49:30Z |
| publishDate | 2017-12-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-b25f1a66236641008561affd96ebeab32022-12-22T02:49:43ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522017-12-013210.15826/umj.2017.2.00340ON \(\Lambda\)-CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIESNikolai Yu. Antonov0Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, EkaterinburgWe consider one type of convergence of multiple trigonometric Fourier series intermediate between the convergence over cubes and the \(\lambda \)-convergence for \(\lambda >1\). The well-known result on the almost everywhere convergence over cubes of Fourier series of functions from the class \( L (\ln ^ + L) ^ d \ln ^ + \ln ^ + \ln ^ + L ([0,2 \pi)^d ) \) has been generalized to the case of the \( \Lambda \)-convergence for some sequences \(\Lambda\).https://umjuran.ru/index.php/umj/article/view/99Trigonometric Fourier series, Rectangular partial sums, Convergence almost everywhere |
| spellingShingle | Nikolai Yu. Antonov ON \(\Lambda\)-CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIES Ural Mathematical Journal Trigonometric Fourier series, Rectangular partial sums, Convergence almost everywhere |
| title | ON \(\Lambda\)-CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIES |
| title_full | ON \(\Lambda\)-CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIES |
| title_fullStr | ON \(\Lambda\)-CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIES |
| title_full_unstemmed | ON \(\Lambda\)-CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIES |
| title_short | ON \(\Lambda\)-CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIES |
| title_sort | on lambda convergence almost everywhere of multiple trigonometric fourier series |
| topic | Trigonometric Fourier series, Rectangular partial sums, Convergence almost everywhere |
| url | https://umjuran.ru/index.php/umj/article/view/99 |
| work_keys_str_mv | AT nikolaiyuantonov onlambdaconvergencealmosteverywhereofmultipletrigonometricfourierseries |