Consider a vector $p$ in $\mathbb{R}^3$ such that $||p||=1$.
Let $f$ in $S(\mathbb{R}^3)$ (you can assume as smooth as you want if desire).
Consider the following operator defined in Fourier by :
$$\widehat{F(f)}(\xi) = \frac{(\xi \cdot p)^2}{|\xi|^2} \hat{f}(\xi).$$
I want to compute the fourier operator $F$ in the physical space. It is of degree zero in $\xi$ so I guess the operator should not involved any derivatives of $f$.
Any help is welcomed, as always.
