Commutators and singular integral operators in Clifford analysis

In this paper we develop a method for setting the compactness of the commutator relative to the singular integral operator acting on Hölder continuous functions over Ahlfors David regular surfaces in R ⁿ⁺¹ . This method is based on the essential use of the monogenic decomposition of Hölder continuous functions. We also set forth explicit representations of the adjoints of the singular Cauchy type integral operators, relative to a total subset of real functionals.