Generalization of the Hardy-Littlewood theorem on Fourier series
In the theory of one-dimensional trigonometric series, the Hardy-Littlewood theorem on Fourier series with monotone Fourier coefficients is of great importance. Multidimensional versions of this theorem have been extensively studied for the Lebesgue space. Significant differences of the mul...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2021-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2021-104-4/5.pdf |
| _version_ | 1797686736111796224 |
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| author | S. Bitimkhan |
| author_facet | S. Bitimkhan |
| author_sort | S. Bitimkhan |
| collection | DOAJ |
| description | In the theory of one-dimensional trigonometric series, the Hardy-Littlewood theorem on Fourier series with monotone Fourier coefficients is of great importance. Multidimensional versions of this theorem have been extensively studied for the Lebesgue space. Significant differences of the multidimensional variants in comparison with the one-dimensional case are revealed and the strengthening of this theorem is obtained. The Hardy-Littlewood theorem is also generalized for various function spaces and various types of monotonicity of the series coefficients. Some of these generalizations can be seen in works of M.F. Timan, M.I. Dyachenko, E.D. Nursultanov, S. Tikhonov. In this paper, a generalization of the Hardy-Littlewood theorem for double Fourier series of a function in the space L_qϕ(L_q)(0,2π]^2 is obtained. |
| first_indexed | 2024-03-12T01:10:12Z |
| format | Article |
| id | doaj.art-d23ab95e49b24077ae062b7d39dcda08 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-12T01:10:12Z |
| publishDate | 2021-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-d23ab95e49b24077ae062b7d39dcda082023-09-14T07:22:19ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112021-12-011044495510.31489/2021M4/49-55Generalization of the Hardy-Littlewood theorem on Fourier seriesS. Bitimkhan In the theory of one-dimensional trigonometric series, the Hardy-Littlewood theorem on Fourier series with monotone Fourier coefficients is of great importance. Multidimensional versions of this theorem have been extensively studied for the Lebesgue space. Significant differences of the multidimensional variants in comparison with the one-dimensional case are revealed and the strengthening of this theorem is obtained. The Hardy-Littlewood theorem is also generalized for various function spaces and various types of monotonicity of the series coefficients. Some of these generalizations can be seen in works of M.F. Timan, M.I. Dyachenko, E.D. Nursultanov, S. Tikhonov. In this paper, a generalization of the Hardy-Littlewood theorem for double Fourier series of a function in the space L_qϕ(L_q)(0,2π]^2 is obtained.https://mathematics-vestnik.ksu.kz/apart/2021-104-4/5.pdf |
| spellingShingle | S. Bitimkhan Generalization of the Hardy-Littlewood theorem on Fourier series Қарағанды университетінің хабаршысы. Математика сериясы |
| title | Generalization of the Hardy-Littlewood theorem on Fourier series |
| title_full | Generalization of the Hardy-Littlewood theorem on Fourier series |
| title_fullStr | Generalization of the Hardy-Littlewood theorem on Fourier series |
| title_full_unstemmed | Generalization of the Hardy-Littlewood theorem on Fourier series |
| title_short | Generalization of the Hardy-Littlewood theorem on Fourier series |
| title_sort | generalization of the hardy littlewood theorem on fourier series |
| url | https://mathematics-vestnik.ksu.kz/apart/2021-104-4/5.pdf |
| work_keys_str_mv | AT sbitimkhan generalizationofthehardylittlewoodtheoremonfourierseries |