# Riesz transform and integration by parts formulas for random variables

- Authors
- Journal
- Stochastic Processes and their Applications 0304-4149
- Publisher
- Elsevier
- Publication Date
- Volume
- 121
- Issue
- 6
- Identifiers
- DOI: 10.1016/j.spa.2011.02.006
- Keywords

## Abstract

Abstract We use integration by parts formulas to give estimates for the L p 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.

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