Boundedness of Calderon Commutators and some generalizations via the method of discretized paraproducts

Abstract: Since Calderon introduced the Calderon Commutators in 1960s, their boundedness and various high dimensional analogues have been established by different methods. One of the modern ways is the method of discretized paraproduct. I will introduce this method and show how this is highly related to the smoothness of the symbol of the multilinear operators, as well as some new results.