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 Lp(W)-boundedness of 𝒱ρ(𝒯n,∗) with norm ∥𝒱ρ(𝒯n,∗)∥Lp(W)→Lp(W) ≤ C[W]Ap1+ 1 p−1− 1 p 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.

中文翻译：

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Calderón–Zygmund 算子与矩阵权重的变化

让p ∈ (1,∞),ρ ∈ (2,∞)和W是一个矩阵一种p重量。在本文中，我们介绍了一个版本的变体𝒱ρ(𝒯n,*)对于具有满足 Dini 条件的连续模的矩阵 Calderón–Zygmund 算子。然后我们得到大号p(W)-有界性𝒱ρ(𝒯n,*)有规范 ∥𝒱ρ(𝒯n,*)∥大号p(W)→大号p(W) ≤ C[W]一种p1+ 1 p-1- 1 p 首先证明标量 Calderón-Zygmund 算子的变分的稀疏支配，然后提供矩阵 Calderón-Zygmund 算子的变分的凸体稀疏支配。这里的关键步骤是关于标量 Calderón-Zygmund 算子的局部最大截断算子的弱类型估计。