  Let D denote the Dirac operator in the Euclidean space R^m. In this paper, we
present a refinement of the biharmonic functions and at the same time an
extension of the monogenic functions by considering the equation DfD=0. The
solutions of this "sandwich" equation, which we call inframonogenic functions,
are used to obtain a new Fischer decomposition for homogeneous polynomials in
R^m.
