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 for the weak type (1, 1) estimate of noncommutative maximal Calderón–Zygmund operators; as an application, we obtain the weak type (1, 1) estimates of operator-valued maximal singular integrals of convolution type under proper regularity conditions. These are the first noncommutative maximal inequalities for families of truly non-positive linear operators. For homogeneous singular integrals, the strong type ( p , p ) ( 1更多