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Is there some kind of function space $X(R^n)$ which satisfies the compact embedding relation as follows: $W^{k,p}(R^n)\hookrightarrow\hookrightarrow X(R^n)$? Could I guess the indeterminate function space $X(R^n)$ be one of the types: $W^{m,q}(R^n)$, $C^{m,\alpha}(R^N)$ etc. ^-^

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Can you rephrase this question? It is not clear to me what you are asking. –  Chris Janjigian Nov 26 '12 at 6:18
@ Chris: I have improved my question. Can you understand it right now? :-) –  Darry Nov 26 '12 at 6:33

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