Abstract
We characterize the surjective isometries of a class of analytic functions on the disk which include the Analytic Besov spaceBp and the Dirichlet spaceDp. In the case ofBp we are able to determine the form of all linear isometries on this space. The isometries for these spaces are finite rank perturbations of integral operators. This is in contrast with the classical results for the Hardy and Bergman spaces where the isometries are represented as weighted compositions induced by inner functions or automorphisms of the disk.
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