David Corfield asked the following questions yesterday: Is the
$n$-dimensional Fourier transform of $\exp(-\|x\|)$ always non-negative,
where $\|\cdot\|$ is the Euclidean norm on $\Bbb R^n$?  What is its support?

I want to ask a more general question: what happens when $\|\cdot\|$ is the
$p$-norm, for arbitrary $p\in [1, 2]$?

David's question is here: <https://mathoverflow.net/questions/723/is-the-fourier-transform-of-exp-x-non-negative>