On the Fourier transform of bump functions

Question

Let us call a non-negative smooth compactly supported function on $\mathbb{R}^n$ which is not identically zero a bump function. My question is: Does there exist a bump function $f$ on $\mathbb{R}^2$ for which the integral $\int_{\mathbb{R}^2}\hat{f}(\xi)\|\xi\|^{-2}d \xi$ is finite? Here $\hat{f}$ stands for the Fourier transform of $f$.