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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2007.10070 |
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| _version_ | 1866911773955719168 |
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| author | Prats, Martí |
| author_facet | Prats, Martí |
| contents | We study the stability of Triebel-Lizorkin regularity of bounded functions and Lipschitz functions under bi-Lipschitz changes of variables and the regularity of the inverse function of a Triebel-Lizorkin bi-Lipschitz map in Lipschitz domains. To obtain the results we provide an equivalent norm for the Triebel-Lizorkin spaces with fractional smoothness in uniform domains in terms of the first-order difference of the last weak derivative available averaged on balls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_10070 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity Prats, Martí Classical Analysis and ODEs 42B35, 47B33 We study the stability of Triebel-Lizorkin regularity of bounded functions and Lipschitz functions under bi-Lipschitz changes of variables and the regularity of the inverse function of a Triebel-Lizorkin bi-Lipschitz map in Lipschitz domains. To obtain the results we provide an equivalent norm for the Triebel-Lizorkin spaces with fractional smoothness in uniform domains in terms of the first-order difference of the last weak derivative available averaged on balls. |
| title | Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity |
| topic | Classical Analysis and ODEs 42B35, 47B33 |
| url | https://arxiv.org/abs/2007.10070 |