Singular Integrals with Monogenic Kernels on the m-Torus and their Lipschitz Perturbations

Explicit transformation formulas between the H^∞-Fourier multipliers on L^p (T ^m ) and the monogenic kernels of the associated singular integrals are given. It is indicated, as a generalization and variation of the Coifman-Mclntosh-Meyer theorem on Lipschitz graphs, that these kernels give rise to bounded operators on Lipschitz perturbations of T ^m .