Abstract

N. Fournier and J. Printems established a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with Hölder
 continuous coefficients. This is of course out of reach by using already classical probabilistic methods based on Malliavin calculus. Recently Debussche and Romito
employed 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 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 diferent framework: we use it in order to estimate the error in total variance
distance in some convergence theorems.