Square Functions Controlling Smoothness and Higher-Order Rectifiability
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913848350474240 |
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| author | Hoffman, John |
| author_facet | Hoffman, John |
| contents | We provide new characterizations of the $BMO$-Sobolev space $I_α(BMO)$ for the range $0 < α<2$. When $0 < α<1$, our characterizations are in terms of square functions measuring multiscale approximation of constants, and when $1 \leq α<2$ our characterizations are in terms of square functions measuring multiscale approximation by linear functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Square Functions Controlling Smoothness and Higher-Order Rectifiability Hoffman, John Classical Analysis and ODEs 28A75, 30L99, 43A85 We provide new characterizations of the $BMO$-Sobolev space $I_α(BMO)$ for the range $0 < α<2$. When $0 < α<1$, our characterizations are in terms of square functions measuring multiscale approximation of constants, and when $1 \leq α<2$ our characterizations are in terms of square functions measuring multiscale approximation by linear functions. |
| title | Square Functions Controlling Smoothness and Higher-Order Rectifiability |
| topic | Classical Analysis and ODEs 28A75, 30L99, 43A85 |
| url | https://arxiv.org/abs/2410.11724 |