Geodesic
Orlicz spaces of differential forms on Riemannian manifolds: duality and cohomology
Problemy analiza, Tome 6 (2017) no. 2, pp. 57-80

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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 $\Delta_2\cap\nabla_2$.
Keywords: Riemannian manifold, differential form, exterior differential, Orlicz space, Orlicz cohomology. 
@article{PA_2017_6_2_a3,
     author = {Ya. A. Kopylov},
     title = {Orlicz spaces of differential forms on {Riemannian} manifolds: duality and cohomology},
     journal = {Problemy analiza},
     pages = {57--80},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2017_6_2_a3/}
}
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Ya. A. Kopylov. Orlicz spaces of differential forms on Riemannian manifolds: duality and cohomology. Problemy analiza, Tome 6 (2017) no. 2, pp. 57-80. http://geodesic.mathdoc.fr/item/PA_2017_6_2_a3/