Orlicz spaces of differential forms on Riemannian manifolds: duality and cohomology

Ya. A. Kopylov

Problemy analiza, Tome 6 (2017) no. 2, pp. 57-80.

Résumé

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-Poincaré duality for reduced $L_{q,p}$-cohomology by Gol'dshtein and Troyanov to $L_{\Phi_I,\Phi_{II}}$-cohomology, where $\Phi_I$ and $\Phi_{II}$ are $N$-functions of class $\Delta_2\cap\nabla_2$.

Détail

Keywords: Riemannian manifold, differential form, exterior differential, Orlicz space, Orlicz cohomology.

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