Sobolev -spaces on -thick closed subsets of

Abstract

Let be a nonempty closed set such that for some and the -Hausdorff content for all cubes with centre and edge length . For each we give an intrinsic characterization of the trace space of the Sobolev space to the set . Furthermore, we prove the existence of a bounded linear operator such that is the right inverse to the standard trace operator. Our results extend those available in the case for Ahlfors-regular sets . Bibliography: 36 titles.