# What does this Fourier multiplicator operator do?

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.