  This paper deals with the operator-valued Hardy spaces introduced and studied
by Tao Mei. Our principal result shows that the Poisson kernel in Mei's
definition of these spaces can be replaced by any reasonable test function. As
an application, we get a general characterization of Hardy spaces on quantum
tori. The latter characterization plays a key role in our recent study of
Triebel-Lizorkin spaces on quantum tori.
