Summary: In this paper, we consider functions satisfying the sandwich equation \(\partial_{\underline{x}} f \partial_{\underline{x}} = 0\), where \(\partial_{\underline{x}}\) stands for the Dirac operator in \(\mathbb{R}^m\). Such functions are referred as inframonogenic and represent an extension of the monogenic functions, i.e., null solutions of \(\partial_{\underline{x}}\).
In particular, for odd \(m\), we prove that a \(C^2\)-function is both inframonogenic and harmonic in \(\operatorname{\Omega} \subset \mathbb{R}^m\) if and only if it can be represented in \(\Omega\) as \[ f = f_1 + f_2 + f_3 \underline{x} + \underline{x} f_4 , \] where \(f_1\) and \(f_2\) are, respectively, left and right monogenic functions in \(\Omega \), while \(f_3\) and \(f_4\) are two-sided monogenic functions there. Finally, in deriving some applications of our results, we have made use of the deep connection between the class of inframonogenic vector fields and the universal solutions of the Lamé-Navier system in \(\mathbb{R}^3\).