A note on the Gaussian maximal functions

2013/11/20 by Teuwen, Jonas
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1311.5032

Abstract

This note presents a proof that the non-tangential maximal function of the Ornstein-Uhlenbeck semigroup is bounded almost surely by the Gaussian Hardy-Littlewood maximal function. In particular this entails improvement on a result by Pineda and Urbina who proved a similar result for a `trunctated' version of the non-tangential maximal function. We actually obtain boundedness of the maximal function on non-tangential cones of arbitrary aperture.

Related

• Non-tangential maximal functions and conical square functions with\n respect to the Gaussian measure
• Non Tangential Convergence for the Ornstein-Uhlenbeck Semigroup
• Boundedness properties of the maximal operator in a nonsymmetric inverse Gaussian setting
• On the maximal function for the generalized Ornstein-Uhlenbeck semigroup
• Maximal and quadratic Gaussian Hardy spaces