An extended Sobolev scale over vector bundles

Abstract

We introduce an extended Sobolev scale over vector bundles on smooth closed manifolds and investigate its interpolation properties. This scale is built on the base of the inner product H\"ormander spaces whose order of regularity is given by an arbitrary positive function RO-varying at infinity. We prove that every space belonging to the scale introduced is obtained by the interpolation with a function parameter between certain Sobolev spaces over the vector bundle. We show that this space does not depend (up to equivalence of norms) on the choice of local charts on manifold and local trivializations of the bundle.