Abstract
We find necessary and sufficient conditions on a Banach spaceX in order for the vector-valued extensions of several operators associated to the Ornstein-Uhlenbeck semigroup to be of weak type (1, 1) or strong type (p, p) in the range 1<p<∞. In this setting, we consider the Riesz transforms and the Littlewood-Paleyg-functions. We also deal with vector-valued extensions of some maximal operators like the maximal operators of the Ornstein-Uhlenbeck and the corresponding Poisson semigroups and the maximal function with respect to the gaussian measure.
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