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MR 290095 · 2015 · DOI 10.1090/s0002-9947-2014-06088-1

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How to Recognise Extension domains

math.FA · 2026-04-26 · unverdicted · novelty 6.0

A bounded domain is a (1,p)-extension domain if and only if it is Ahlfors regular and satisfies (1-s)[f]_{W^{s,p}(Ω)}^p ≤ C [f]_{W^{1,p}(Ω)}^p for all f in the homogeneous Sobolev space and s near 1.

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  • How to Recognise Extension domains math.FA · 2026-04-26 · unverdicted · none · ref 3

    A bounded domain is a (1,p)-extension domain if and only if it is Ahlfors regular and satisfies (1-s)[f]_{W^{s,p}(Ω)}^p ≤ C [f]_{W^{1,p}(Ω)}^p for all f in the homogeneous Sobolev space and s near 1.