Lack of interpolation of linear operators in spaces of smooth functions

B. S. Mityagin ; E. M. Semenov

Izvestiya. Mathematics , Tome 11 (1977) no. 6, pp. 1229-1266.

Résumé

We prove that $C^k(\Omega)$, the space of $k$ times continuously differentiable functions on the closure of a region in a finite-dimensional manifold, is not an interpolation space between $C(\Omega)$ and $C^n(\Omega)$ for $0$. We find analogous results for the Sobolev–Stein spaces. In the class of spaces $C_\varphi$, defined by the modulus of continuity, we describe all interpolation spaces between $C$ and $C^2$. Bibliography: 34 titles.

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