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

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

2010-03-22

arxiv.org/abs/1003.4092v2

Mathematics

Functional Analysis

21 pages, revised version with various arguments simplified and generalised

Scientific paper

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.

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