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 L^p(dgamma)-boundedness properties, being dgamma the Gauss
measure. We achieve our results by looking at the oscillation and variation operators from a vector valued point of view.