Higher Order Gradients of Monogenic Functions

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