Sobolev extension by linear operators

By Charles Fefferman, Arie Israel, Garving K. Luli. 2012

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Let L(R) be the Sobolev space of functions with mth derivatives lying in L(R). Assume that n < p < ∞. For E ⊂ R, let L(E) denote the space of restrictions to E of functions in L(R). We show that there exists a bounded linear map T : Lm,p(E)→ L(R) such that, for any f ∈ L(E), we have Tf = f on E. We also give a formula for the order of magnitude of ‖f‖Lm,p(E) for a given f : E→ R when E is finite.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4f192b7fa21cfa8dffbe319a1ccd1a24a64692a1