Weak type $(1,1)$ estimates for noncommutative rough homogeneous singular integrals

We establish the weak type $(1,1)$ endpoint estimate for operator-valued rough homogeneous singular integrals with kernels satisfying the classical $L\log L$ integrability and cancellation conditions. This extends Seeger’s endpoint theorem [{J. Amer. Math. Soc.} $\mathbf{\text{9}}$ (1996)] to the noncommutative setting. A key ingredient is an off-diagonal analysis that controls interactions between different kernel scales and avoids an additional logarithmic loss.