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arxiv: 0806.2430 · v1 · submitted 2008-06-15 · 🧮 math.FA

Sobolev W¹_p-spaces on closed subsets of R^n

classification 🧮 math.FA
keywords closedsobolevarbitrarycharacterizationsdoublinggiveintrinsiclocal
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For each $p>n$ we use local oscillations and doubling measures to give intrinsic characterizations of the restriction of the Sobolev space $W_p^1(R^n)$ to an arbitrary closed subset of $R^n$.

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