  In [18] Fournier and Printems establish a methodology which allows to prove
the absolute continuity of the law of the solution of some stochastic equations
with H\"{o}lder continuous coefficients. This is of course out of reach by
using already classical probabilistic methods based on Malliavin calculus. In
[11] Debussche and Romito employ some Besov space technics in order to
substantially improve the result of Fournier and Printems. In our paper we show
that this kind of problem naturally fits in the framework of interpolation
spaces: we prove an interpolation inequality (see Proposition 2.5) which allows
to state (and even to slightly improve) the above absolute continuity result.
Moreover it turns out that the above interpolation inequality has applications
in a completely different framework: we use it in order to estimate the error
in total variance distance in some convergence theorems.
