Degree-independent Sobolev extension on locally uniform domains

We consider the problem of constructing extensions , where 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 non-rectifiable boundaries, a k-dependent family of operators was constructed by Jones. In this work we produce a k-independent operator for all spaces on a locally uniform domain Ω.