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arXiv · 2104.04240

Higher order gradients of monogenic functions

Luca Baracco·Stefano Pinton
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Abstract

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.

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Luca Baracco, Stefano Pinton. 2021-04-09. Higher order gradients of monogenic functions. https://arxiv.org/abs/2104.04240

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