2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119340The notion of $L^p$-distributions is introduced on Riemannian symmetric spaces of noncompact type and their main properties are established. We use a geometric description for the topology of the space of test functions in terms of the Laplace-Beltrami operator. The techniques are based on a-priori estimates for elliptic operators. We show that structure theorems, similar to $\Rn$, hold on symmetric spaces. We give estimates for the convolutions.Functional AnalysisDifferential Geometry46F05; 46F10; 53C21; 53C35text