The Hodge decomposition is well-known for compact manifolds. The result has been extended by Kodaira to non-compact complete manifolds in the space of L 2 forms. This decomposition was done in the Sobolev space H1 (Λk (Hn (−a 2 ))), in [4], on a space form of constant negative sectional curvature. In this thesis we extend the decomposition to the Sobolev space Hl (Λk (Hn (−a 2 ))), for integers n ≥ 2, l ≥ 0, n ≥ k ≥ 0. We also prove that this decomposition holds in the strong sense, depending on n and k, the dimension and the degree of the differential form.</p
