2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73374Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian acting on m-forms in the Poincaré space is found. Also, by means of some estimates for hyperbolic singular integrals, we obtain L^p-estimates for the Riesz transforms passing from the Laplacian to other covariant derivatives, in a range of p depending on m,n. Finally, using these, it is shown that the Laplacian defines topological isomorphisms in the scale of form Sobolev spaces, for m different from n/2,(n+1)/2,(n-1)/2.To appear in Indiana Univ. Math. JAnalysis of PDEsDifferential Geometry53C21, 58J05, 58J50, 58J70text