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 [[DELTA].sub.2] intersection] [nabla]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. Bibliography: 21 titles.
1 Introduction Let [B.sub.1] and [B.sub.2] be Banach spaces. We denote by T: [B.sub.1] [right arrow] [B.sub.2] a closed operator on a linear subspace D(T) of [B.sub.1]. An operator T [...]