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

Abstract

We study, in L 1 (R n ; γ) with respect to the gaussian measure, nontangential 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.

Locations

• Publicacions Matemàtiques - View
• Dipòsit Digital de Documents de la UAB (Universitat Autònoma de Barcelona) - View - PDF