H-B Theorems of Cauchy Integral Operators in Clifford Analysis

In this article, we verify the boundedness of the Cauchy type integral operators under the generalized Hölder norm in Clifford analysis, which are called H-B theorems of the Cauchy integral operators in Clifford analysis. We first demonstrate the generalized 2P theorems and the generalized Muskhelishvili theorem in Clifford analysis by Du’s method derived from Du (J Math (PRC) 2(2):115–12, 1982) and Lu (Boundary value problems of analytic functions. World Scientific, Singapore, 1993), which greatly refines the coefficients estimate of inequality in Du et al. (Acta Math Sci 29B(1):210–224, 2009) and Zhang (Complex Var Elliptic Equ 52(6):455–473, 2007). Then, we obtain the H-B theorems which extend and improve the corresponding results in Du et al. (2009) and Wang and Du (Z Anal Anwend, 2024).