The B–P Formula and Cauchy Integral Formula for Weighted Inframonogenic Functions\(\dag \)

Abstract

In this paper, in order to study the B–P formula of weighted inframonogenic functions, two important lemmas are first given, which solve the difficulty caused by the non commutativity of Clifford valued functions in multiplication operations. Then, using the conclusion of the above lemmas and the relationship between  \(\textrm{d}\sigma \)  under non-Euclidean distances and  \(\textrm{d}\mu _{r}\)  under Euclidean distances, the B–P formula for weighted inframonogenic functions is obtained by digging out singularities to satisfy the conditions for using the Stokes formula, and introducing new operators to simplify the calculation steps. Furthermore, the Cauchy integral formula for weighted inframonogenic functions is obtained.