Calder\'{o}n commutators and the Cauchy integral on Lipschitz curves revisited I. First commutator and generalizations

This article is the first in a series of three papers, whose scope is to give new proofs to the well known theorems of Calder\'{o}n, Coifman, McIntosh and Meyer. Here we treat the case of the first commutator and some of its generalizations.