CONICAL SQUARE FUNCTIONS AND NON-TANGENTIAL MAXIMAL FUNCTIONS WITH RESPECT TO THE GAUSSIAN MEASURE

We study, in L(1) (R(n); gamma) with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated 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 L(1)-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.