  We introduce and investigate classes of normed or quasinormed distribution
spaces of generalized smoothness that can be obtained by various interpolation
methods applied to classical Sobolev, Nikolskii-Besov, and Triebel-Lizorkin
spaces. An arbitrary positive function O-regularly varying at infinity serves
as the order of regularity for the spaces introduced. They are broad
generalizations of the above classical spaces and allow being well defined on
smooth manifolds. We give applications of the spaces under investigation to
elliptic equations and elliptic problems on smooth manifolds.

Analysis of PDEs;Functional Analysis