Weak $(1,1)$ estimate for maximal truncated rough singular integral operator
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909814324461568 |
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| author | Lai, Xudong |
| author_facet | Lai, Xudong |
| contents | In their seminal work (Amer. J. Math. 78: 289-309, 1956), Calderón and Zygmund introduced the maximal truncated rough singular integral operator and established its $L^p$-boundedness for $1 < p < \infty$. However, the endpoint case $p = 1$ remained an open problem. This paper resolves this problem. More precisely, we prove that the maximal truncated rough singular integral operator is of weak type $(1,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak $(1,1)$ estimate for maximal truncated rough singular integral operator Lai, Xudong Classical Analysis and ODEs Analysis of PDEs In their seminal work (Amer. J. Math. 78: 289-309, 1956), Calderón and Zygmund introduced the maximal truncated rough singular integral operator and established its $L^p$-boundedness for $1 < p < \infty$. However, the endpoint case $p = 1$ remained an open problem. This paper resolves this problem. More precisely, we prove that the maximal truncated rough singular integral operator is of weak type $(1,1)$. |
| title | Weak $(1,1)$ estimate for maximal truncated rough singular integral operator |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2508.17737 |