Integral formulas and Teodorescu transform for generalized partial-slice monogenic functions

TL;DR

This paper develops integral formulas and studies the Teodorescu transform within the framework of generalized partial-slice monogenic functions, blending Clifford analysis and slice monogenic functions.

Contribution

It introduces and analyzes integral formulas and properties of the Teodorescu transform for a new class of functions combining Clifford and slice monogenic theories.

Findings

Derived Cauchy and Plemelj formulas for generalized partial-slice monogenic functions

Established properties of the Teodorescu transform in this context

Provided norm estimates for the Teodorescu transform

Abstract

The theory of generalized partial-slice monogenic functions is considered as a syhthesis of the classical Clifford analysis and the theory of slice monogenic functions. In this paper, we investigate the Cauchy integral formula and the Plemelj formula for generalized partial-slice monogenic functions. Further, we study some properties of the Teodorescu transform in this context. A norm estimation for the Teodorescu transform is discussed as well.