  We consider a functional on the Wiener space which is smooth and not
degenerated in Malliavin sense and we give a criterion of strict positivity of
the density. We also give lower bounds for the density. These results are based
on the representation of the density by means of the Riesz transform introduced
by Malliavin and Thalmaier and on the estimates of the Riesz transform given
Bally and Caramellino.
