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We consider a functional on the Wiener space which is smooth and notdegenerated in Malliavin sense and we give a criterion of strict positivity ofthe density. We also give lower bounds for the density. These results are basedon the representation of the density by means of the Riesz transform introducedby Malliavin and Thalmaier and on the estimates of the Riesz transform givenBally and Caramellino.

Positivity and lower bounds for the density of Wiener functionals