On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis

Euclidean Clifford analysis is a higher dimensional function theory, refining harmonic analysis, centred around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator, called the Dirac operator. More recently, Hermitean Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions of two Hermitean Dirac operators, invariant under the action of the unitary group. In this paper, a Cauchy integral formula is established by means of a matrix approach, allowing the recovering of the traditional Martinelli-Bochner formula for holomorphic functions of several complex variables as a special case.