Conical square functions and non-tangential maximal functions with respect to the gaussian measure

We study, in L¹(R̃ⁿ; γ) with respect to the gaussian measure, non- tangential maximal functions and conical square functions associ- ated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in L¹-norm by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda.