Convolution inequality with weak Lp

I had the pleasure to stumble upon a "well-known convolution inequality": $$\iint u(x)u(y)f(x-y)dxdy \leq C_1||u||_r^2||f||_{p,\infty}$$ The integrals are over $\mathbb{R}^n \times \mathbb{R}^n$, $r = (2p)/(2p-1)$ and $||\cdot||_{p,\infty}$ is just the weak $L^p$ space. I tried proving it by truncating (in respect to $f = f\mathbb{1}_{|f|>\alpha} + f\mathbb{1}_{|f|\leq \alpha}$) then applying Young on the two sums. I did not succeed in finding the above expression, especially I did not manage to "only" find $u$ in respect to the $L^r$ norm... Any help, ideas or a reference are very much appreciated!