(1) Faculty of Mathematics and Informatic, University of Holguín, Holguín, 80100, Cuba;(2) Faculty of Mathematics and Computer Science, University of Oriente, Santiago of Cuba, 90500, Cuba
Abstract:
The main goal of this paper is centred around the study of the behavior of the Cauchy type integral and its corresponding
singular version, both over nonsmooth domains in Euclidean space. This approach is based on a recently developed quaternionic
Cauchy integrals theory 1, 5, 7] within the three-dimensional setting. The present work involves the extension of fundamental
results of the already cited references showing that the Clifford singular integral operator has a proper invariant subspace
of generalized H?lder continuous functions defined in a surface of the (m+1)-dimensional Euclidean space.