  In this paper we prove structural and topological characterizations of the
screened Sobolev spaces with screening functions bounded below and above by
positive constants. We generalize a method of interpolation to the case of
seminormed spaces. This method, which we call the truncated method, generates
the screened Sobolev subfamily and a more general screened Besov scale. We then
prove that the screened Besov spaces are equivalent to the sum of a Lebesgue
space and a homogeneous Sobolev space and provide a Littlewood-Paley frequency
space characterization.
