Sobolev Embedding Theorem for the Sobolev-Morrey spaces
In this paper we prove a Sobolev Embedding Theorem for Sobolev-Morrey spaces. The proof is based on the Sobolev Integral Representation Theorem and on a recent results on Riesz potentials in generalized Morrey spaces of Burenkov, Gogatishvili, Guliyev, Mustafaev and on estimates on the Riesz potent...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2016-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/99 |
| _version_ | 1797372622964523008 |
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| author | V.I. Burenkov N.A. Kydyrmina |
| author_facet | V.I. Burenkov N.A. Kydyrmina |
| author_sort | V.I. Burenkov |
| collection | DOAJ |
| description |
In this paper we prove a Sobolev Embedding Theorem for Sobolev-Morrey spaces. The proof is based on the Sobolev Integral Representation Theorem and on a recent results on Riesz potentials in generalized Morrey spaces of Burenkov, Gogatishvili, Guliyev, Mustafaev and on estimates on the Riesz potentials. We mention that a Sobolev Embedding Theorem for Sobolev morrey spaces had been proved by Campanato, for a subspace of our Sobolev-Morrey space which corresponds to the closure of the set of smooth functions in our Sobolev-Morrey space. The methods of the present paper are considerably different from those of Campanato.
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| first_indexed | 2024-03-08T18:38:29Z |
| format | Article |
| id | doaj.art-f38c8ab8ccca456693e34694a820c702 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:29Z |
| publishDate | 2016-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-f38c8ab8ccca456693e34694a820c7022023-12-29T10:21:59ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112016-09-01833Sobolev Embedding Theorem for the Sobolev-Morrey spacesV.I. BurenkovN.A. Kydyrmina In this paper we prove a Sobolev Embedding Theorem for Sobolev-Morrey spaces. The proof is based on the Sobolev Integral Representation Theorem and on a recent results on Riesz potentials in generalized Morrey spaces of Burenkov, Gogatishvili, Guliyev, Mustafaev and on estimates on the Riesz potentials. We mention that a Sobolev Embedding Theorem for Sobolev morrey spaces had been proved by Campanato, for a subspace of our Sobolev-Morrey space which corresponds to the closure of the set of smooth functions in our Sobolev-Morrey space. The methods of the present paper are considerably different from those of Campanato. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/99Morrey spaceSobolev-Morrey spaceSobolev Embedding Theorem |
| spellingShingle | V.I. Burenkov N.A. Kydyrmina Sobolev Embedding Theorem for the Sobolev-Morrey spaces Қарағанды университетінің хабаршысы. Математика сериясы Morrey space Sobolev-Morrey space Sobolev Embedding Theorem |
| title | Sobolev Embedding Theorem for the Sobolev-Morrey spaces |
| title_full | Sobolev Embedding Theorem for the Sobolev-Morrey spaces |
| title_fullStr | Sobolev Embedding Theorem for the Sobolev-Morrey spaces |
| title_full_unstemmed | Sobolev Embedding Theorem for the Sobolev-Morrey spaces |
| title_short | Sobolev Embedding Theorem for the Sobolev-Morrey spaces |
| title_sort | sobolev embedding theorem for the sobolev morrey spaces |
| topic | Morrey space Sobolev-Morrey space Sobolev Embedding Theorem |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/99 |
| work_keys_str_mv | AT viburenkov sobolevembeddingtheoremforthesobolevmorreyspaces AT nakydyrmina sobolevembeddingtheoremforthesobolevmorreyspaces |