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

J. Maas, J. Van Neerven, P. Portal, Publicacions Matemàtiques 55 (2011) 313–341.


Journal Article | Published
Author
Maas, JanIST Austria ; van Neerven, Jan M; Portal, Pierre
Abstract
We study, in L1(R̃n; γ) with respect to the gaussian measure, non- tangential maximal functions and conical square functions associ- ated 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 L1-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.
Publishing Year
Date Published
2011-07-01
Journal Title
Publicacions Matemàtiques
Acknowledgement
The first named author is supported by Rubicon subsidy 680-50-0901 of the Netherlands Organisation for Scientific Research (NWO). The second named author is supported by VICI subsidy 639.033.604 of the Netherlands Organisation for Scientific Research (NWO
Volume
55
Issue
2
Page
313 - 341
IST-REx-ID

Cite this

Maas J, Van Neerven J, Portal P. Conical square functions and non-tangential maximal functions with respect to the Gaussian measure. Publicacions Matemàtiques. 2011;55(2):313-341. doi:10.5565/PUBLMAT_55211_03 
Maas, J., Van Neerven, J., & Portal, P. (2011). Conical square functions and non-tangential maximal functions with respect to the Gaussian measure. Publicacions Matemàtiques, 55(2), 313–341. https://doi.org/10.5565/PUBLMAT_55211_03 
Maas, Jan, Jan Van Neerven, and Pierre Portal. “Conical Square Functions and Non-Tangential Maximal Functions with Respect to the Gaussian Measure.” Publicacions Matemàtiques 55, no. 2 (2011): 313–41. https://doi.org/10.5565/PUBLMAT_55211_03  .
J. Maas, J. Van Neerven, and P. Portal, “Conical square functions and non-tangential maximal functions with respect to the Gaussian measure,” Publicacions Matemàtiques, vol. 55, no. 2, pp. 313–341, 2011.
Maas J, Van Neerven J, Portal P. 2011. Conical square functions and non-tangential maximal functions with respect to the Gaussian measure. Publicacions Matemàtiques. 55(2), 313–341.
Maas, Jan, et al. “Conical Square Functions and Non-Tangential Maximal Functions with Respect to the Gaussian Measure.” Publicacions Matemàtiques, vol. 55, no. 2, Universitat Autònoma de Barcelona, Departament de Matemàtique, 2011, pp. 313–41, doi:10.5565/PUBLMAT_55211_03  .
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