A note on the Gaussian maximal functions
Analysis of PDEs
2014-08-06 v2 Functional Analysis
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.
Cite
@article{arxiv.1311.5032,
title = {A note on the Gaussian maximal functions},
author = {Jonas Teuwen},
journal= {arXiv preprint arXiv:1311.5032},
year = {2014}
}