Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms
Viviane Baladi, Masato Tsujii (2007)
Annales de l’institut Fourier
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We study spectral properties of transfer operators for diffeomorphisms on a Riemannian manifold . Suppose that is an isolated hyperbolic subset for , with a compact isolating neighborhood . We first introduce Banach spaces of distributions supported on , which are anisotropic versions of the usual space of functions and of the generalized Sobolev spaces , respectively. We then show that the transfer operators associated to and a smooth weight extend boundedly to these...