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On the compactness of the hypercomplex commutator in hölder continuous functions spaces

Abstract:

This paper is devoted to the compactness of the hypercomplex commutator SγMa-MaSγ, where Sγ is the Cauchy singular integral operator (in the Douglis sense), a is a Hölder continuous hypercomplex function and Ma is the multiplication operator given by Maf=af. 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. © Birkhäuser Verlag Basel/Switzerland 2009.