Weak type $(1,1)$ boundedness of noncommutative singular integral operators with rough kernels

In this paper, we establish the weak type $(1,1)$ boundedness of noncommutative singular integral operators with rough kernels. To deal with the rough kernels, we develop some orthogonality of the kernels themselves in the pseudo-localization arguments for the good functions and use the microlocal decomposition and $T{T}^{\ast }$ arguments for the bad functions.