2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78283We show that a homogeneous convolution kernel on an arbitrary homogeneous group which is L \log L on the unit annulus is bounded on L^p for 1 < p < \infty and is of weak-type (1,1), generalizing the result of Seeger. The proof is in a similar spirit to that of Christ and Rubio de Francia.28 pages, no figures, to appear Indiana Math J., final versionClassical Analysis and ODEs42B20text