  Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise
in many areas of analysis, stochastic analysis in particular. We prove an
embedding into certain q-variation spaces and discuss a few applications. First
we show q-variation regularity of Cameron-Martin paths associated to fractional
Brownian motion and other Volterra processes. This is useful, for instance, to
establish large deviations for enhanced fractional Brownian motion. Second, the
q-variation embedding, combined with results of rough path theory, provides a
different route to a regularity result for stochastic differential equations by
Kusuoka. Third, the embedding theorem works in a non-commutative setting and
can be used to establish Hoelder/variation regularity of rough paths.
