Clifford Algebras, Fourier Theory, Singular Integrals, and Harmonic Functions on Lipschitz Domains

This is a slightly expanded version of my lectures at the conference on Clifford Algebras in Analysis held in Fayetteville, Arkansas. I present an exposition of basic material on Clifford algebras, monogenic functions, and singular integrals with monogenic kernels. Then follow results from the paper “Clifford algebras, Fourier transforms, and singular convolution operators on Lipschitz surfaces” by Chun Li, Tao Qian and myself [LMcQ]. Here is an edited excerpt from its introduction.