Variation of CalderónZygmund operators with matrix weight

Let p (1,∞), ρ (2,∞) and W be a matrix Ap weight. In this paper, we introduce a version of variation Vρ(Tn, - ∗) for matrix Calderón-Zygmund operators with modulus of continuity satisfying the Dini condition. We then obtain the L^p(W)-boundedness of Vρ(Tn, - ∗) with norm (equation presented) by first proving a sparse domination of the variation of the scalar Calderón-Zygmund operator, and then providing a convex body sparse domination of the variation of the matrix Calderón-Zygmund operator. The key step here is a weak type estimate of a local grand maximal truncated operator with respect to the scalar Calderón-Zygmund operator.