# When Dirac function is in $H^{-m}(R^n)$?

If Dirac function $\delta\in H^{-m}(R^n)$,please give the range of $m$?

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This is a very reasonable question... downvotes are a mystery. – paul garrett Jan 2 '13 at 13:41
@Paul Although guessing reasons for downvotes isn't a productive activity, I remark that despite the presence of mathematical content, the question completely lacks the poster's thoughts on said content. Maybe it was written in a hurry and Darry will do better next time. This one has been answered already. – user53153 Jan 2 '13 at 16:20

Hint: the Fourier transform of $\delta_0$ is the constant equal to $1$. So the problem is to see whether $(1+|x|^2)^{s/2}$ is integrable over $\Bbb R^n$. As this function is radial, we can reduce this to a problem of integration over the real line.