Normal and Compact Solvability of the Exterior Derivation Operator in Orlicz Spaces

We study the normal and compact solvability of the operator of exterior derivation in Orlicz spaces of differential forms on compact Riemannian manifolds. We prove the compact solvability of the exterior derivation operator defined on an Orlicz space of differential forms corresponding to a Δ 2 ∩ ∇...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-10, Vol.276 (1), p.98-110
Main Author: Kopylov, Ya. A.
Format: Article
Language:English
Subjects:
Derivation
Mathematics
Mathematics and Statistics
Operators (mathematics)
Orlicz space
Riemann manifold
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Summary:We study the normal and compact solvability of the operator of exterior derivation in Orlicz spaces of differential forms on compact Riemannian manifolds. We prove the compact solvability of the exterior derivation operator defined on an Orlicz space of differential forms corresponding to a Δ 2 ∩ ∇ 2 -regular N-function on a compact oriented smooth Riemannian manifold considered on its maximal and minimal domains containing all smooth forms with compact support.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06727-0