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We study, in $L^{1}(\R^n;\gamma)$ with respect to the gaussian measure,non-tangential maximal functions and conical square functions associated withthe Ornstein-Uhlenbeck operator by developing a set of techniques which allowus, to some extent, to compensate for the non-doubling character of thegaussian measure. The main result asserts that conical square functions can becontrolled in $L^1$-norm by non-tangential maximal functions. Along the way weprove a change of aperture result for the latter. This complements recentresults on gaussian Hardy spaces due to Mauceri and Meda.

Non-tangential maximal functions and conical square functions with respect to the Gaussian measure