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The structure of Sobolev extension operators

Author(s): Fefferman, Charles L.; Israel, Arie; Luli, Garving K

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Abstract: Let L-m,L-p (R-n) denote the Sobolev space of functions whose m-th derivatives lie in L-p (R-n), and assume that p > n. For E subset of R-n, denote by L-m,L-p (E) the space of restrictions to E of functions F is an element of L-m,L-p (R-n). It is known that there exist bounded linear maps T : L-m,L-p (E) -> L-m,L-p (R-n) such that T f = f on E for any f is an element of L-m,L-p (E). We show that T cannot have a simple form called “bounded depth”.
Publication Date: 2014
Electronic Publication Date: 8-Jul-2014
Citation: Fefferman, Charles, Israel, Arie, Luli, Garving K. (2014). The structure of Sobolev extension operators. REVISTA MATEMATICA IBEROAMERICANA, 30 (419 - 429. doi:10.4171/RMI/787
DOI: doi:10.4171/RMI/787
ISSN: 0213-2230
Pages: 419 - 429
Type of Material: Journal Article
Version: Author's manuscript

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