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

Jan Maas, Jan van Neerven, and Pierre Portal

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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.

Article information

Source
Publ. Mat., Volume 55, Number 2 (2011), 313-341.

Dates
First available in Project Euclid: 22 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.pm/1308748950

Mathematical Reviews number (MathSciNet)
MR2839445

Zentralblatt MATH identifier
1226.42013

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42B30: $H^p$-spaces 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Keywords
Hardy spaces Gaussian measure Ornstein-Uhlenbeck operator square function maximal function

Citation

Maas, Jan; van Neerven, Jan; Portal, Pierre. Conical square functions and non-tangential maximal functions with respect to the gaussian measure. Publ. Mat. 55 (2011), no. 2, 313--341. https://projecteuclid.org/euclid.pm/1308748950


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