On the inequality of different metrics for trigonometric polynomials
The article is devoted to the research question of inequalities for different metrics with trigonometric polynomials. The structure of this exploring, its main components and types, as well as its classical approaches are presented in this article. Nikolsky’s inequalities in different metrics are w...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2019-03-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/293 |
| _version_ | 1797372693328166912 |
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| author | G.A. Yessenbayeva А.N. Yesbayev H. Poppell |
| author_facet | G.A. Yessenbayeva А.N. Yesbayev H. Poppell |
| author_sort | G.A. Yessenbayeva |
| collection | DOAJ |
| description |
The article is devoted to the research question of inequalities for different metrics with trigonometric polynomials. The structure of this exploring, its main components and types, as well as its classical approaches are presented in this article. Nikolsky’s inequalities in different metrics are well known for trigonometric polynomials. In this paper, inequalities of different metrics are proved in the Lorentz and Lebesgue spaces for trigonometric polynomials of one variable. A similar result is obtained for trigonometric polynomials of many variables. The article is focused mainly on mathematicians.
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| first_indexed | 2024-03-08T18:38:32Z |
| format | Article |
| id | doaj.art-fc0c35401efc4d5cab1fd49e4db71b4d |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:32Z |
| publishDate | 2019-03-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-fc0c35401efc4d5cab1fd49e4db71b4d2023-12-29T10:20:58ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112019-03-0193110.31489/2019m1/102-107On the inequality of different metrics for trigonometric polynomialsG.A. YessenbayevaА.N. YesbayevH. Poppell The article is devoted to the research question of inequalities for different metrics with trigonometric polynomials. The structure of this exploring, its main components and types, as well as its classical approaches are presented in this article. Nikolsky’s inequalities in different metrics are well known for trigonometric polynomials. In this paper, inequalities of different metrics are proved in the Lorentz and Lebesgue spaces for trigonometric polynomials of one variable. A similar result is obtained for trigonometric polynomials of many variables. The article is focused mainly on mathematicians. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/293Lebesgue spacesLorentz spacestrigonometric polynomialsinequalities of different metrics |
| spellingShingle | G.A. Yessenbayeva А.N. Yesbayev H. Poppell On the inequality of different metrics for trigonometric polynomials Қарағанды университетінің хабаршысы. Математика сериясы Lebesgue spaces Lorentz spaces trigonometric polynomials inequalities of different metrics |
| title | On the inequality of different metrics for trigonometric polynomials |
| title_full | On the inequality of different metrics for trigonometric polynomials |
| title_fullStr | On the inequality of different metrics for trigonometric polynomials |
| title_full_unstemmed | On the inequality of different metrics for trigonometric polynomials |
| title_short | On the inequality of different metrics for trigonometric polynomials |
| title_sort | on the inequality of different metrics for trigonometric polynomials |
| topic | Lebesgue spaces Lorentz spaces trigonometric polynomials inequalities of different metrics |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/293 |
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