标题： 弱 $(1,1)$ 估计对于极大截断粗糙奇异积分算子 显示英文标题

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

摘要： 在他们的开创性工作（Amer. J. Math. 78: 289-309, 1956）中，Calderón 和 Zygmund 引入了最大截断的粗糙奇异积分算子，并建立了其对于$L^p$的有界性对于$1 < p < \infty$。然而，端点情况$p = 1$仍然是一个开放问题。本文解决了这个问题。更准确地说，我们证明了最大截断的粗糙奇异积分算子是弱类型的$(1,1)$。 显示英文摘要

摘要： 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 $(1,1)$.