Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $2 \le q \le \infty$ and $2s >n$, then is there a continuous embedding $ H^s (\Bbb R^n ) \hookrightarrow L^q(\Bbb R^n) $ ? Here $H^s$ means a general Sobolev space for $s = 0,1,\cdots$.

share|cite|improve this question
    
I think the conclusion holds if and only if q=2 – sun Dec 1 '12 at 11:38
    
@DavideGiraudo Thank you for the comment! Would you recommend a book or some documents involving some Sobolev inequalities on the domain $\Bbb R^n$ ? – Karl Dec 1 '12 at 14:14
    
Maybe Evans' book Partial differential equations. I rememmber Willie Wong has written notes on Sobolev spaces, so the result is almost surely in these ones. – Davide Giraudo Dec 1 '12 at 14:16
    
@DavideGiraudo Thank you very much. – Karl Dec 1 '12 at 14:17

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.