Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori

This paper studies 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.