Integral formulas and Hodge decomposition in the theory of generalized partial-slice mo-nogenic functions

TL;DR

This paper develops integral formulas, operator symbols, and Hodge decomposition for generalized slice monogenic functions, expanding analytical tools and extending the Teodorescu transform within this mathematical framework.

Contribution

It introduces new integral formulas, operator symbols, and extends the Teodorescu transform to generalized slice monogenic functions, establishing Hodge decomposition in this context.

Findings

Extended the Teodorescu transform for generalized functions

Established Hodge decomposition for the function class

Provided new integral and representation formulas

Abstract

This paper explores generalized slice monogenic functions by introducing their operator symbols, representation formula, and integral formula. The study extends the Teodorescu transform to a broader class of theorems and inferences, providing new analytical tools for function theory in this setting. Additionally, the Hodge decomposition is established, providing a foundation for further research.