I know $\textrm{vp} \left( \dfrac{1}{x} \right)$ is a distribution of order exactly $1$ on $\mathbb{R}$.
Therefore $\textrm{vp} \left( \dfrac{1}{x} \right) \otimes \textrm{vp} \left( \dfrac{1}{x} \right) $ is of order at most $2$ on $\mathbb{R}^2$; but is it exactly $2$ ?
I can't find a sequence of functions which would help me prove that it is (nor can I prove that the order is at most 1).
Thank you for your help.