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We introduce and investigate classes of normed or quasinormed distributionspaces of generalized smoothness that can be obtained by various interpolationmethods applied to classical Sobolev, Nikolskii-Besov, and Triebel-Lizorkinspaces. An arbitrary positive function O-regularly varying at infinity servesas the order of regularity for the spaces introduced. They are broadgeneralizations of the above classical spaces and allow being well defined onsmooth manifolds. We give applications of the spaces under investigation toelliptic equations and elliptic problems on smooth manifolds.

Interpolation spaces of generalized smoothness and their applications to elliptic equations