2021
DOI: 10.48550/arxiv.2109.03770
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The norm of linear extension operators for $C^{m-1,1}(\mathbb{R}^n)$

Abstract: Fix integers m ≥ 2, n ≥ 1. Let C m−1,1 (R n ) be the space of (m − 1)times differentiable functions F : R n → R whose (m − 1)'st order partial derivatives are Lipschitz continuous, equipped with a standard seminorm. Given E ⊆ R n , let C m−1,1 (E) be the trace space of all restrictions F |E of functions F in C m−1,1 (R n ), equipped with the standard quotient (trace) seminorm. We prove that there exists a bounded linear operator T :with operator norm at most exp(γD k ), where D := m+n−1 n is the number of mult… Show more

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