2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68698The main objective of the paper is to prove a geometric version of sharp trace and product estimates on null hypersurfaces with finite curvature flux. These estimates play a crucial role to control the geometry of such null hypersurfaces. The paper is based on an invariant version of the classical Littlewood -Paley theory, in a noncommutative setting, defined via heat flow on surfaces.Analysis of PDEsDifferential Geometrytext