Refined localization spaces, Kondratiev spaces with fractional smoothness and extension operators
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929339302412288 |
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| author | Hansen, Markus Schneider, Cornelia |
| author_facet | Hansen, Markus Schneider, Cornelia |
| contents | In this paper, we introduce Kondratiev spaces of fractional smoothness based on their close relation to refined localization spaces. Moreover, we investigate relations to other approaches leading to extensions of the scale of Kondratiev spaces with integer order of smoothness, based on complex interpolation, and give further results for complex interpolation of those function spaces. As it turns out to be one of the main tools in studying these spaces on domains of polyhedral type, certain aspects of the analysis of Stein's extension operator are revisited. Finally, as an application, we study Sobolev-type embeddings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Refined localization spaces, Kondratiev spaces with fractional smoothness and extension operators Hansen, Markus Schneider, Cornelia Numerical Analysis Functional Analysis In this paper, we introduce Kondratiev spaces of fractional smoothness based on their close relation to refined localization spaces. Moreover, we investigate relations to other approaches leading to extensions of the scale of Kondratiev spaces with integer order of smoothness, based on complex interpolation, and give further results for complex interpolation of those function spaces. As it turns out to be one of the main tools in studying these spaces on domains of polyhedral type, certain aspects of the analysis of Stein's extension operator are revisited. Finally, as an application, we study Sobolev-type embeddings. |
| title | Refined localization spaces, Kondratiev spaces with fractional smoothness and extension operators |
| topic | Numerical Analysis Functional Analysis |
| url | https://arxiv.org/abs/2405.06316 |