Let us $f(x) \in C^\infty $ on $\mathbb{R}^n$, and the pseudo-diff. operator $ Q$ is defined by: $(Qu)(x)=(2\pi)^{-n}\int_{\mathbb{R}^{n}}e^{ix\xi }f(x)\left | \xi \right |\hat{u}(\xi) d\xi$
Where the operator is elliptic, and what is wave front set: WF(u), if is known that $Qu\in C^\infty $ ?
I know that the symbol of $Q$ is $|\xi|$ and the order of $Q$ is 1.. I need help with this question, how do I show where the operator is elliptic, and what is the way to compute its wave front set?
Thanks!