Dirac operators, conformal transformations and aspects of classical harmonic analysis

Abstract: The main thrust of this paper is to investigate the intimate link between the conformal group and singular integral operators, in particular, but not exclusively, operators of Calderón--Zygmund type, together with associated commutators acting on the $L^{2}$ spaces of surfaces. Clifford analysis and Dirac operators are the basic tools used to help to unify these themes. These surfaces lie in euclidean space, the sphere or the hyperbola. We illustrate how these results extend to a general class of submanifolds with arbitrary codimension in euclidean space, the sphere or the hyperbola.

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