2024/06/03 by Andreas Rosén, Rosén, Andreas
Mathematics · #42B20 #42B35 #42B37 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2406.01776
openalex publication_date 2024/06/03 · openalex created_date 2024/06/08 · openalex updated_date 2026/07/28
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 From this a non-standard sparse domination of the singular integrals is established, where averages have been replaced by Carleson averages.