  We study an alternative definition of the $H_1$-space associated to a
semicommutative von Neumann algebra $L_\infty(\mathbb{R}) \overline{\otimes}
\mathcal{M}$, first studied by Mei. We identify a "new" description for atoms
in $H_1$. We then explain how they can be used to study $H_1^c$-$L_1$ endpoint
estimates for Calder\'on-Zygmund operators with noncommuting kernels.
