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This article is cited in 2 scientific papers (total in 2 papers)
Orlicz spaces of differential forms on Riemannian manifolds: duality and cohomology
Ya. A. Kopylovab a Novosibirsk State University,
2, Pirogova st., Novosibirsk 630090, Russia
b Sobolev Institute of Mathematics,
4, Akad. Koptyuga st., Novosibirsk 630090, Russia
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-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.
Received: 12.05.2017 Revised: 06.10.2017 Accepted: 30.08.2017
Citation:
Ya. A. Kopylov, “Orlicz spaces of differential forms on Riemannian manifolds: duality and cohomology”, Probl. Anal. Issues Anal., 6(24):2 (2017), 57–80
Linking options:
https://www.mathnet.ru/eng/pa217 https://www.mathnet.ru/eng/pa/v24/i2/p57
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Abstract page: | 199 | Full-text PDF : | 67 | References: | 31 |
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