In this talk, I will talk about two weight estimates for commutators. This topic is initiated from the work by Bloom in 1985, who studied the Hilbert transform case, and resumed recently by Holmes, Lacey and Wick by providing the related estimates for the Riesz transform. Since then this topic has attracted a lot of attentions. We continue this research line, by extending and developing the topic to the multilinear setting.

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