A system of quaternionic equations in four-dimensional complex space

The boundary properties are studied of a class of quaternionic functions containing the class of holomorphic functions of four variables. A condition is found in order for a function defined on some five- or six-dimensional part of the whole topological boundary $\partial D$ of a domain $D\subset C^4$ of a special type to have a holomorphic continuation. The results obtained are used to solve singular integral equations in $C^4$.