Riemann boundary value problems on half space in Clifford analysis

In this paper, we discuss some properties of the Cauchy type integral operator defined over the half space of . As applications, we study a type of Riemann boundary value problem for solutions to polynomially generalized Cauchy–Riemann equations including with and as special cases over the half space of . Making use of Fischer‐type decomposition and the Clifford calculus for solutions to these equations, we will obtain explicit expressions of solutions to the kind of boundary value problems over the half space of . Copyright © 2012 John Wiley & Sons, Ltd.