Title: Maximal singular integral operators acting on noncommutative Lp-spaces
Speaker: Bang Xu (Wuhan University)
Time: 15:00-16:00, August21
Location: Tecent Meeting, Tecent Meeting ID: 943 221 490
Abstract: In this talk, we study the boundedness theory for maximal Calderon-Zygmund operators acting on noncommutative Lp-spaces. Our first result is a criterion for the weak type (1,1) estimate of noncommutative maximal Calderon-Zygmund operators; as an application, we obtain the weak type (1,1) estimates of operator-valued maximal convolution singular integrals under proper regularity conditions. These are the first noncommutative maximal results for families of linear operators that can’t be reduced to positive ones. For homogeneous singular integrals, the strong type (p, p) (1< p < ∞) maximal estimates are shown to be true even for rough kernels.
As a byproduct of the criteria, we obtain the noncommutative weak type (1,1) estimate for Calderon-Zygmund operators with integral regularity condition which is slightly stronger than the Hormander condition; this provides some evidence to an affirmative answer of an open question posed by Parcet. This is joint work with Guixiang Hong and Xudong Lai.
