Laurent Expansion and L2-Boundary Values in Hermitian Clifford Analysis.

Inspired by the classical Cauchy transform in L 2 (∂ B (R)) , we first derive the Laurent expansion for Hermitian monogenic functions in Hermitian Clifford analysis, and we obtain direct applications of this expansion. Then we use the Laurent expansion to study the L 2 -boundary values of Hermitian monogenic functions, we prove that every f ∈ L 2 (S 2 m - 1 ; V) can be decomposed as a sum of boundary values of functions, which are h-monogenic inside and outside the unit ball respectively. [ABSTRACT FROM AUTHOR]