A maximal function characterisation of the Hardy space for the Gauss measure

Abstract

In dimension one we give a maximal function characterisation of the Hardy space H^1(g) for the Gauss measure g, introduced by G. Mauceri and S. Meda. In arbitrary dimension, we give a description of the nonnegative functions in H^1(g) and use it to prove that L^p(g) is a contained in H^1(g) for 1<p\le\infty.

15 pages

References in corpus (1)

• Non-tangential maximal functions and conical square functions with respect to the Gaussian measure