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

• Autores: Jan Maas, Jan van Neerven, Pierre Portal
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 55, Nº 2, 2011, págs. 313-340
• Idioma: inglés
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• Resumen

  • We study, in L1(Rn; ) 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.