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 ρ(n, ) for matrix CalderónZygmund operators with modulus of continuity satisfying the Dini condition. We then obtain the Lp(W)boundedness of ρ(n, ) with norm ρ(n, )Lp(W)→Lp(W) ≤ C[W]Ap1+ 1 p1 1 p by first proving a sparse domination of the variation of the scalar CalderónZygmund operator, and then providing a convex body sparse domination of the variation of the matrix CalderónZygmund operator. The key step here is a weak type estimate of a local grand maximal truncated operator with respect to the scalar CalderónZygmund operator.