  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.
