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

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.

26 pages