The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothness
The theory of embedding of spaces of differentiable functions studies the important relations of differential (smoothness) properties of functions in various metrics and has a wide application in the theory of boundary value problems of mathematical physics, approximation theory, and other...
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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 |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/456 |
| _version_ | 1797372641460355072 |
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| author | K.A. Bekmaganbetov K.Ye. Kervenev Ye. Toleugazy |
| author_facet | K.A. Bekmaganbetov K.Ye. Kervenev Ye. Toleugazy |
| author_sort | K.A. Bekmaganbetov |
| collection | DOAJ |
| description |
The theory of embedding of spaces of differentiable functions studies the important relations of differential (smoothness) properties of functions in various metrics and has a wide application in the theory of boundary value problems of mathematical physics, approximation theory, and other fields of mathematics. In this article, we prove the embedding theorems for anisotropic spaces Nikol’skii-Besov with a generalized mixed smoothness and mixed metric, and anisotropic Lorentz spaces. The proofs of the obtained results are based on the inequality of different metrics for trigonometric polynomials in Lebesgue spaces with mixed metrics and interpolation properties of the corresponding spaces.
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| first_indexed | 2024-03-08T18:38:47Z |
| format | Article |
| id | doaj.art-3595268fe1cc468e8aad96104bc05906 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:47Z |
| publishDate | 2021-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-3595268fe1cc468e8aad96104bc059062023-12-29T10:19:42ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112021-12-01104410.31489/2021m4/28-34The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothnessK.A. BekmaganbetovK.Ye. KervenevYe. Toleugazy The theory of embedding of spaces of differentiable functions studies the important relations of differential (smoothness) properties of functions in various metrics and has a wide application in the theory of boundary value problems of mathematical physics, approximation theory, and other fields of mathematics. In this article, we prove the embedding theorems for anisotropic spaces Nikol’skii-Besov with a generalized mixed smoothness and mixed metric, and anisotropic Lorentz spaces. The proofs of the obtained results are based on the inequality of different metrics for trigonometric polynomials in Lebesgue spaces with mixed metrics and interpolation properties of the corresponding spaces. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/456anisotropic Lorentz spacesanisotropic Nikol’skii-Besov spacesgeneralized mixed smoothnessmixed metricembedding theorems |
| spellingShingle | K.A. Bekmaganbetov K.Ye. Kervenev Ye. Toleugazy The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothness Қарағанды университетінің хабаршысы. Математика сериясы anisotropic Lorentz spaces anisotropic Nikol’skii-Besov spaces generalized mixed smoothness mixed metric embedding theorems |
| title | The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothness |
| title_full | The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothness |
| title_fullStr | The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothness |
| title_full_unstemmed | The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothness |
| title_short | The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothness |
| title_sort | embedding theorems for anisotropic nikol skii besov spaces with generalized mixed smoothness |
| topic | anisotropic Lorentz spaces anisotropic Nikol’skii-Besov spaces generalized mixed smoothness mixed metric embedding theorems |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/456 |
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