Oscillation and variation for the Gaussian Riesz transforms and Poisson integral

Abstract

For the family of truncations of the Gaussian Riesz transforms and Poisson integral we study their rate of convergence through the oscillation and variation operators. More precisely, we search for their Lp (dγ)-boundedness properties, where dγ denotes the Gauss measure. We achieve our results by looking at the oscillation and variation operators from a vector-valued point of view.