Consider the p-Laplacian operator $\Delta_{p}u:= div(|\nabla u|^{p-2}\nabla u)$, where $1<p<\infty$. We know when $p=2$, it's the standard laplacian operator. So my question is what is the fourier transform of this operator. For general Laplacian, I know $\widehat {\Delta u}(\xi)=|\xi|^2 \hat u(\xi)$. What is $\widehat {\Delta_{p} u}(\xi)$?
I couldn't find relevant notes and only find this link: https://mathoverflow.net/questions/228009/backgrounds-of-the-p-laplacian-operator