A quaternionic Beltrami-type equation and the existence of local homeomorphic solutions

The paper deals with a quaternionic Beltrami-type equation, which is a very natural generalization of the complex Beltranni equation to higher dimensi ons. Special attention is paid to the systematic use of the embedding of th e set of quaternions H into C-2 and tho corresponding application of matrix singular integral operators. The proof of the existence of local homeomorp hic solutions is based on a necessary and sufficient criterion, which relat es the Jacobian determinant of a mapping from R-4 into R-4 to the quaternio nic derivative of a monogenic function.