De Rham regularization operators in Orlicz spaces of differential forms on Riemannian manifolds

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.