Clifford wavelets, Hardy spaces, and elliptic boundary value problems

Abstract

We give an overview of results concerning certain boundary value problems for elliptic Partial Differential Equations on nonsmooth domains, Clifford algebras, and wavelet techniques, and how these are related. In particular, we consider Laplace’s equation on nonsmooth domains and show how this leads to wavelet analysis of certain Clifford algebra valued singular integral operators. A natural context for stuying these operators is the theory of Hardy spaces of Clifford analytic functions, which we discuss in some detail. General elliptic operators are also considered.