  Given a monogenic function on the quaternionic algebra $\mathbb{H}$, the
Clifford algebra $\mathbb{R}_n$ or the octonionic algebra $\mathbb{O}$ we prove
that $|\nabla^m f|^\alpha$ is subharmonic for some $\alpha>0$ where $\nabla^m
f$ is the $m$-th order gradient of $f$. We find also the optimal value of
$\alpha$. This is generalization of a result of Calderon and Zygmund.
