Whitney extension operators without loss of derivatives

Leonhard Frerick; Enrique Jordá; Jochen Wengenroth

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arXiv · 1304.2928

Whitney extension operators without loss of derivatives

Leonhard Frerick·Enrique Jordá·Jochen Wengenroth

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Abstract

For a compact set, we characterize the existence of a linear extension operator E for the space of Whitney jets without loss of derivatives, that is, E satisfies the best possible continuity estimates: The supremum of all partial derivatives up to order n of E(f) is less or equal than a constant times the n-th Whitney norm of f. The characterization is a surprisingly simple purely geometric condition telling in a way that at all its points, the set is big enough in all directions.

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Leonhard Frerick, Enrique Jordá, Jochen Wengenroth. 2013-04-10. Whitney extension operators without loss of derivatives. https://arxiv.org/abs/1304.2928

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