  We obtain new oscillation inequalities in metric spaces in terms of the
Peetre $K-$functional and the isoperimetric profile. Applications provided
include a detailed study of Fractional Sobolev inequalities and the
Morrey-Sobolev embedding theorems in different contexts. In particular we
include a detailed study of Gaussian measures as well as probablity measures
between Gaussian and exponential. We show a kind of reverse Polya-Szego
principle that allows us to obtain continuity as a self improvement from
boundedness, using symetrization inequalities. Our methods also allow for
precise estimates of growth envelopes of generalized Sobolev and Besov spaces
on metric spaces. We also consider embeddings into $BMO$ and their connection
to Sobolev embeddings.
