ORLICZ SPACES OF DIFFERENTIAL FORMS ON RIEMANNIAN MANIFOLDS: DUALITY AND COHOMOLOGY

Abstract

We consider Orlicz spaces of differential forms on a Riemannian manifold. A Riesz-type theorem about the functionals on Orlicz spaces of forms is proved and other duality theorems are obtained therefrom. We also extend the results on the Hölder-Poincarè duality for reduced L_q,_p-cohomology by Gol`dshtein and Troyanov to Lᵩᵢ ,ᵩᵢᵢ -cohomology, where Φᵢ and Φᵢᵢ are N-functions of class ∆2 ∩ ∇2.

Keywords

• Riemannian manifold
• differential form
• exterior differential
• Orlicz space