2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170208We establish a theory for the existence and regularity of solutions to the cohomological equation over an accessible, partially hyperbolic diffeomorphism. As a by-product of our techniques, we show that for $r>1$, any $C^r$ homogeneous, locally compact submanifold of a $C^r$ manifold is in fact a $C^r$ submanifold.94 pages, 8 figuresDynamical SystemsGeometric Topology37C15; 37D30text