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arXiv · 2508.17737

Weak $(1,1)$ estimate for maximal truncated rough singular integral operator

Xudong Lai
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Abstract

In their seminal work (Amer. J. Math. 78: 289-309, 1956), Calder\'on 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 $(1,1)$.

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Xudong Lai. 2025-08-25. Weak $(1,1)$ estimate for maximal truncated rough singular integral operator. https://arxiv.org/abs/2508.17737

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