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- W3081321774 abstract "For each $p > 1$ and each positive integer $m$, we give intrinsic characterizations of the restriction of the homogeneous Sobolev space $L_{p}^{m}(mathbb{R})$ to an arbitrary closed subset $E$ of the real line. We show that the classical one-dimensional Whitney extension operator is universal for the scale of $L{p}^{m}(mathbb{R})$ spaces in the following sense: For every $pin(1,infty]$, it provides almost optimal $L^m_p$-extensions of functions defined on $E$. The operator norm of this extension operator is bounded by a constant depending only on $m$. This enables us to prove several constructive $L^m_p$-extension criteria expressed in terms of $m$-th order divided differences of functions._" @default.
- W3081321774 created "2020-09-01" @default.
- W3081321774 creator A5017275709 @default.
- W3081321774 date "2020-08-26" @default.
- W3081321774 modified "2023-09-25" @default.
- W3081321774 title "Extension criteria for homogeneous Sobolev spaces of functions of one variable" @default.
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- W3081321774 doi "https://doi.org/10.4171/rmi/1210" @default.
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