Degree-independent Sobolev extension on locally uniform domains

We consider the problem of constructing extensions L p k (Ω)→L p k (Rn), where L p k is the Sobolev space of functions with k derivatives in Lp and Ω ⊂ Rn is a domain. In the case of Lipschitz Ω, Calderón gave a family of extension operators depending on k, while Stein later produced a single (k-independent) operator. For the more general class of locally-uniform domains, which includes examples with highly nonrectifiable boundaries, a k-dependent family of operators was constructed by Jones. In this work we produce a k-independent operator for all spaces L p k (Ω) on a locally uniform domain Ω. © 2005 Elsevier Inc. All rights reserved.