This article is the last in a series of three papers, whose aim is to give new proofs of the well-known theorems of Calderón, Coifman, McIntosh and Meyer (,  and ). Here we extend the results of the previous two papers to the polydisc setting. In particular, we solve completely a question of Coifman open since the nineteen-eighties.
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Camil Muscalu, Calderón commutators and the Cauchy integral on Lipschitz curves revisited III. Polydisc extensions. Rev. Mat. Iberoam. 30 (2014), no. 4, pp. 1413–1437DOI 10.4171/RMI/820