2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77170Weighted norm estimates and representation formulas are proved for non-homogeneous singular integrals with no regularity condition on the kernel and only an L log L integrability condition. The representation formulas involve averages over a star-shaped set naturally associated with the kernel. The proof of the norm estimates is based on the representation formulas, some new variations of the Hardy-Littlewood maximal function, and weighted Littlewood-Paley theory.32 pages, 2 figuresClassical Analysis and ODEs42B20; 42B25text