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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.13772 |
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| _version_ | 1866911926875848704 |
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| author | Hoang, Cong Moen, Kabe Pérez, Carlos |
| author_facet | Hoang, Cong Moen, Kabe Pérez, Carlos |
| contents | We extend the subrepresentation formula $$ |f(x)|\le c_n\,I_1(|\nabla f|)(x) $$ in several ways. First, we consider more general $A_1$-potential operators on the right-hand side and prove local and global pointwise inequalities for these operators. Second, we show that we can improve the right-hand side using fractional derivatives. Finally, we extend our results to rough singular integral operators, similar to the main result in [HMP1]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new look at subrepresentation formulas Hoang, Cong Moen, Kabe Pérez, Carlos Classical Analysis and ODEs We extend the subrepresentation formula $$ |f(x)|\le c_n\,I_1(|\nabla f|)(x) $$ in several ways. First, we consider more general $A_1$-potential operators on the right-hand side and prove local and global pointwise inequalities for these operators. Second, we show that we can improve the right-hand side using fractional derivatives. Finally, we extend our results to rough singular integral operators, similar to the main result in [HMP1]. |
| title | A new look at subrepresentation formulas |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2406.13772 |