Clifford Wavelets, Singular Integrals, and Hardy Spaces

This monograph discusses the extensions of basic Fourier analysis to the Clifford algebra framework. Topics covered include: construction of Clifford-valued wavelets; Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces; and Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results are applied to potential theory and elliptic boundary value problems on non-smooth domains. The book is self-contained to a large extent and suited to graduate students and researchers in the areas of wavelet theory, harmonic and Clifford analysis. It should also interest specialists concerned with the application of the Clifford algebra machinery to mathematical physics.