Isometries of Some Banach Spaces of Analytic Functions
We characterize the surjective isometrics of a class of analytic functions on the disk which include the Analytic Besov space B-p and the Dirichlet space D-p. In the case of B-p we are able to determine the form of all linear isometrics on this space. The isometrics 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 isometrics are represented as weighted compositions induced by inner functions or automorphisms of the disk.
Integral Equations and Operator Theory
Hornor, W. E.,
Jamison, J. E.
(2001). Isometries of Some Banach Spaces of Analytic Functions. Integral Equations and Operator Theory, 41(4), 410-425.
Available at: http://aquila.usm.edu/fac_pubs/3728