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2011 Conical square functions and non-tangential maximal functions with respect to the gaussian measure
Jan Maas, Jan van Neerven, Pierre Portal
Publ. Mat. 55(2): 313-341 (2011).

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.

Citation

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Jan Maas. Jan van Neerven. Pierre Portal. "Conical square functions and non-tangential maximal functions with respect to the gaussian measure." Publ. Mat. 55 (2) 313 - 341, 2011.

Information

Published: 2011
First available in Project Euclid: 22 June 2011

zbMATH: 1226.42013
MathSciNet: MR2839445

Subjects:
Primary: 42B25
Secondary: 42B30, 60J35

Rights: Copyright © 2011 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.55 • No. 2 • 2011
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