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

Abstract

We study, in $L^1({\mathbb{R}}^n;\gamma )$ 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.

21 pages, revised version with various arguments simplified and generalised

References in corpus (1)

• Non Tangential Convergence for the Ornstein-Uhlenbeck Semigroup

Cited by in corpus (1)

• A maximal function characterisation of the Hardy space for the Gauss measure