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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 $s = 0,1,\cdots$.

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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

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