Geodesic
De Rham regularization operators in Orlicz spaces of differential forms on Riemannian manifolds
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 361-371.

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In his classical monograph Variétés Différentiables (Paris: Hermann, 1955), G. de Rham introduced smoothing operators on currents on a differentiable manifold. We study some properties of the restrictions of these operators to Orlicz spaces of differential forms on a Riemannian manifold. In particular, we prove that if an $N$-function $\Phi$ is $\Delta_2$-regular then the $L_\Phi$-cohomology of a Riemannian manifold can be calculated with the use of smooth $L^\Phi$-forms.
Keywords: Riemannian manifold, differential form, de Rham regularization operator, Orlicz space, operator of exterior derivation, $L_\Phi$-cohomology. 
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Ya. A. Kopylov; R. A. Panenko. De Rham regularization operators in Orlicz spaces of differential forms on Riemannian manifolds. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 361-371. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a82/

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