If Dirac function $\delta\in H^{-m}(R^n)$,please give the range of $m$?
2026-04-09 05:46:00.1775713560
When Dirac function is in $H^{-m}(R^n)$?
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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.