We prove sharp weighted estimates for the non-tangential maximal function of singular integrals mapping functions from \({\textbf{R}}^n\) to the half-space in \({\textbf{R}}^{1+n}\) above \({\textbf{R}}^n\) . The proof is based on pointwise sparse domination of the adjoint singular integrals that map functions from the half-space back to the boundary. It is proved that these map \(L_1\) functions in the half-space to weak \(L_1\) functions on the boundary. From this a non-standard sparse domination of the singular integrals is established, where averages have been replaced by Carleson averages.
