2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59885Associated to the class of restricted-weak type weights for the Hardy operator, we find a new class of Lorentz spaces for which the normability property holds. This result is analogous to the characterization given by Sawyer for the classical Lorentz spaces. We also show that these new spaces are very natural to study the existence of equivalent norms described in terms of the maximal function16 pagesClassical Analysis and ODEsFunctional Analysis46E30, 26D10text