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

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