On (φ, ψ)-Inframonogenic Functions in Clifford Analysis

Solutions of the sandwich equation (phi)(partial derivative) under bar [f](psi)(partial derivative) under bar = 0, where (phi)(partial derivative) under bar stands for the Dirac operator with respect to a structural set phi, are referred to as (phi, psi)-inframonogenic functions and capture the standard inframonogenic ones as special case. We derive a new integral representation formula for such functions as well as for multidimensional Ahlfors-Beurling transforms closely connected to the use of two different orthogonal basis in R-m. Moreover, we also establish sufficient conditions for the solvability of a jump problem for the system (phi)(partial derivative) under bar [f](psi)(partial derivative) under bar = 0 in domains with fractal boundary.