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What exactly is the content of Sobolev Embedding Theorems (compact for Sobolev spaces and Hölder spaces) when we're looking at functions on the real line?

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    I am not exactly sure what you are asking about; but Sobolev embedding in one dimension is essentially just fundamental theorem of calculus + Hölder inequality + (optionally) interpolation of Lebesgue spaces. The statement of the theorem can be easily checked on, say, [Wikipedia](http://en.wikipedia.org/wiki/Sobolev_inequality#Sobolev_embedding_theorem), so I guess you are not just asking for the statement(s). Can you clarify what you mean by "the content"? (What do you seek in an answer?)2012-09-03

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