Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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
up vote 2 down vote accepted

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.

share|cite|improve this answer
@ Davide Giraudo:Thank you! – Darry Jan 2 '13 at 13:16

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.