2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72342We characterize the rearrangement invariant spaces for which there exists a non-constant fixed point, for the Hardy-Littlewood maximal operator (the case for the spaces $L^p(\mathbb{R}^{n})$ was first considered by Korry in \cite{Ko}). The main result that we prove is that the space $L^{\frac{n}{n-2},\infty}(\mathbb{R}^{n})\cap L^{\infty}(\mathbb{R}^{n})$ is minimal among those having this property8 pagesClassical Analysis and ODEsFunctional Analysis42B25; 46E30text