Sharp Weighted Non-tangential Maximal Estimates via Carleson-Sparse Domination

Journal article, 2024

We prove sharp weighted estimates for the non-tangential maximal function of singular integrals mapping functions from Rn to the half-space in R1+n above Rn. 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 L1 functions in the half-space to weak L1 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 From this a non-standard sparse domination of the singular integrals is established, where averages have been replaced by Carleson averages.