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

Solutions of the sandwich equation ϕ ∂ ̲ [ f ] ψ ∂ ̲ = 0 , where ϕ ∂ ̲ stands for the Dirac operator with respect to a structural set ϕ , are referred to as (ϕ , ψ) -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 ϕ ∂ ̲ [ f ] ψ ∂ ̲ = 0 in domains with fractal boundary. [ABSTRACT FROM AUTHOR]