On operator valued Hardy spaces

Abstract

The note shows that the operator-valued Hardy space $\sH^1$ introduced via Littlewood-Paley $g$-function coincides with the space of $H^1_R(\T, \sL^1)$ of all Bochner integrable operator-valued functions with integrable analytic part. The proof is based on the noncommutative maximal inequality for Poisson group.

This paper has been withdrawn by the author. The current argument has an error. The current result implies that every Calderon-Zygmund operator is bounded on H^1(T, S^1) which is, in fact, not the case