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

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. In this talk, we show our recent result which resolves this problem. More precisely, we prove that the maximal truncated rough singular integral operator is of weak type $(1,1)$.