Wavelet Characterizations of Operator-Valued Hardy Spaces

Abstract

Abstract Let $\mathcal {M}$ be a von Neumann algebra equipped with a normal semifinite faithful trace $\tau $, and $H_{p}(\mathbb {R},\,\mathcal {M}) (1\leq p<\infty )$ be the operator-valued Hardy spaces introduced by Tao Mei. In this paper, we characterize the operator-valued column Hardy space $H^c_{p}(\mathbb {R},\,\mathcal {M}) (1\leq p<\infty )$ by using several square functions involving wavelets, which corresponds to Meyer’s wavelet characterizations of the classical Hardy space when $p=1$.