De Rham Regularization Operators in Orlicz Spaces of Differential Forms on Riemannian Manifolds

摘要

In his classical monograph Vari′et′es Diff′erentiables (Paris:Hermann, 1955), G. de Rham introduced smoothing operators on currentson a differentiable manifold. We study some properties of the restrictionsof these operators to Orlicz spaces of differential forms on a Riemannianmanifold. In particular, we prove that if an N-function Φ is Δ2-regularthen the L -cohomology of a Riemannian manifold can be calculatedwith the use of smooth L -forms.