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

Abstract:

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 Rm. 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.

Año de publicación:

2022

Keywords:

• inframonogenic functions
• Π -Operator
• Clifford analysis
• structural sets

Fuente:

scopus