De rham regularization operators in orlicz spaces of differential forms on Riemannian manifolds

Yaroslav Anatol evich Kopylov, Roman Anatol evich Panenko

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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 Φ is Δ2-regular then the LΦ-cohomology of a Riemannian manifold can be calculated with the use of smooth LΦ-forms.

Original languageEnglish
Pages (from-to)361-371
Number of pages11
JournalSiberian Electronic Mathematical Reports
Volume12
StatePublished - 1 Jan 2015
Externally publishedYes

Keywords

  • De Rham regularization operator
  • Differential form
  • L-cohomology
  • Operator of exterior derivation
  • Orlicz space
  • Riemannian manifold

ASJC Scopus subject areas

  • General Mathematics

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