Higher order gradients of monogenic functions (Q2061525)

Monogenic functions play an essential role in hypercompelex analysis. In this paper it is shown that the interated action of the gradient \(\nabla\) of a monogenic functions \(f\) satisfies that \(|\nabla^m f|^{\alpha}\) is subharmonic for some \(\alpha>0\). Moreover, the optimal value of \(\alpha\) is found in quaternionic, octonionic and Clifford analysis settings. The obtained results generalize a result due to \textit{A. P. Calderon} and \textit{A. Zygmund} [Antoni Stud. Math. 24, 211--226 (1964; 0168.37002)].