Abstract In this paper, we extend the mixed weak-type inequalities of Sawyer type for Calderon-Zygmund operators to the variation operators of θ-type Calderon-Zygmund operators. Moreover, the corresponding quantitative weighted bounds as well as the weighted estimates in the extreme case p = ∞ are also obtained. Meanwhile, we also present the quantitative Bloom type estimate and C p estimates for variation operators of commutators.

中文翻译：

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奇异积分和换向器的加权变异不等式

摘要 在本文中，我们将Calderon-Zygmund 算子的Sawyer 型混合弱型不等式推广到θ 型Calderon-Zygmund 算子的变分算子。此外，还获得了相应的量化加权界限以及极端情况下 p = ∞ 的加权估计。同时，我们还给出了换向器变分算子的定量布隆类型估计和 C p 估计。