On the Compactness of the Hypercomplex Commutator in Hölder Continuous Functions Spaces

Abstract

This paper is devoted to the compactness of the hypercomplex commutator Sγ Ma − MaSγ, where Sγ is the Cauchy singular integral operator (in the Douglis sense), a is a Holder continuous hypercomplex function and Ma is the multiplication operator given by Ma f = a f. We extend a known compactness sufficient condition for the commutator of the Cauchy singular integral operator to the frame of the hypercomplex analysis, where γ is merely required to be an arbitrary regular closed Jordan curve.