Maximal singular integral operators acting on noncommutative $$L_p$$-spaces

In this paper, we study the boundedness theory for maximal Calderón–Zygmund operators acting on noncommutative $$L_p$$ -spaces. Our first result is a criterion weak type (1, 1) estimate of operators; as an application, obtain estimates operator-valued singular integrals convolution under proper regularity conditions. These are inequalities families truly non-positive linear operators. For homogeneous integrals, strong (p, p) ( $$1<p<\infty $$ ) shown to be true even rough kernels. As byproduct criterion, with integral condition that slightly stronger than Hörmander condition; provides somewhat affirmative answer open question in theory.