This article is the first in a series of three papers, whose aim is to give new proofs to the well-known theorems of Calderón, Coifman, McIntosh and Meyer ,  and 5]. Here we treat the case of the first commutator of Calderón and some of its generalizations.
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Camil Muscalu, Calderón commutators and the Cauchy integral on Lipschitz curves revisited I. First commutator and generalizations. Rev. Mat. Iberoam. 30 (2014), no. 2, pp. 727–750