Whitney extension operators without loss of derivatives
Leonhard Frerick
Universität Trier, GermanyEnrique Jordá
Universidad Politécnica de Valencia, Alcoy (Alicante), SpainJochen Wengenroth
Universität Trier, Germany
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Abstract
For a compact set we characterize the existence of a linear extension operator for the space of Whitney jets without loss of derivatives, that is, it satisfies the best possible continuity estimates
where denotes the -th Whitney norm. The characterization is by a surprisingly simple purely geometric condition introduced by Jonsson, Sjögren, and Wallis: there is such that, for every and , there are points in satisfying for all .
Cite this article
Leonhard Frerick, Enrique Jordá, Jochen Wengenroth, Whitney extension operators without loss of derivatives. Rev. Mat. Iberoam. 32 (2016), no. 2, pp. 377–390
DOI 10.4171/RMI/888