Riesz transform and integration by parts formulas for random variables

We use integration by parts formulas to give estimates for the LpLp norm of the Riesz transform. This is motivated by the representation formula for conditional expectations of functionals on the Wiener space already given in Malliavin and Thalmaier (2006) [13]. As a consequence, we obtain regularity and estimates for the density of non-degenerated functionals on the Wiener space. We also give a semi-distance which characterizes the convergence to the boundary of the set of the strict positivity points for the density.