  The trace spaces of Sobolev spaces and related fractional smoothness spaces
have been an active area of research since the work of Nikolskii, Aronszajn,
Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we
review the literature concerning such results for a variety of weighted
smoothness spaces. For this purpose, we present a characterization of the trace
spaces (of fractional order of smoothness), based on integral averages on
dyadic cubes, which is well adapted to extending functions using the Whitney
extension operator.
