On Tempered Ultradistributions in Classical Sobolev Spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908287746703360 |
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| author | Amaonyeiro, A. U. Egwe, M. E. |
| author_facet | Amaonyeiro, A. U. Egwe, M. E. |
| contents | We construct and investigate the properties of tempered ultradistribution spaces in Sobolev spaces. A new Sobolev space preserving the original properties and condition whose derivatives are linear continuous operators embedding in $L^p$ for $1\leq p\leq \infty$ is characterized. Moreover, we also consider some Sobolev embedding theorems involving rapidly decreasing functions, and finally, we prove the extension of Rellich's compactness theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Tempered Ultradistributions in Classical Sobolev Spaces Amaonyeiro, A. U. Egwe, M. E. Functional Analysis 46F10, 46E10, 46F05, 46F20, 46F25 We construct and investigate the properties of tempered ultradistribution spaces in Sobolev spaces. A new Sobolev space preserving the original properties and condition whose derivatives are linear continuous operators embedding in $L^p$ for $1\leq p\leq \infty$ is characterized. Moreover, we also consider some Sobolev embedding theorems involving rapidly decreasing functions, and finally, we prove the extension of Rellich's compactness theorem. |
| title | On Tempered Ultradistributions in Classical Sobolev Spaces |
| topic | Functional Analysis 46F10, 46E10, 46F05, 46F20, 46F25 |
| url | https://arxiv.org/abs/2406.16912 |