Abstract: In this talk, we will introduce a new approach to study the behavior of the (weighted) composition operators acting on Bergman spaces via sparse dominations. New criteria of boundedness and compactness will be characterized. Moreover, we will also derive a new type of weighted estimates associated to the (weighted) composition operators. This talk is based several joint works with Brett Wick, Songxiao Li, Zhenghui Huo and Yecheng Shi.
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