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2015

The Whitney extension theorem in high dimensions

Chang, Alan

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We prove a variant of the standard Whitney extension theorem for $\mathcal C^m(\mathbb R^n)$, in which the norm of the extension operator has polynomial growth in $n$ for fixed $m$.

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Hassler Whitney, Analytic extensions of differentiable functions defined in closed sets , Transactions of the American Mathematical Society 36
Original
1934
Earlier work this paper cites.
Georges Glaeser, Étude de quelques algèbres tayloriennes , J. Analyse Math. 6
1958
Earlier work this paper cites.

Similar

Elias M. Stein, Chapter VI: Extensions and restrictions , Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970, pp. 166–195. MR 0290095 (44 #7280)
1970
Cited alongside, same era.
John C. Wells, Differentiable functions on Banach spaces with Lipschitz derivatives , Journal of Differential Geometry 8
1973
Cited alongside, same era.

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Erwan Le Gruyer, Minimal Lipschitz extensions to differentiable functions defined on a Hilbert space , Geom. Funct. Anal. 19
2009
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