Molecules and Calder\'on-Zygmund operators with noncommuting kernels on $\mathrm{H}_1^c$

Abstract

We study the description of semicommutative Hardy spaces in terms of molecules. We use this characterization to obtain $\mathrm{H}_1^c - \mathrm{H}_1^c$ estimates for Calder\'on-Zygmund operators with kernels with values in a semifinite von Neumann algebra $\mathcal{M}$.