Title

Isometries of Some Banach Spaces of Analytic Functions

Document Type

Article

Publication Date

12-1-2001

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

We characterize the surjective isometries of a class of analytic functions on the disk which include the Analytic Besov spaceB p and the Dirichlet spaceD p. In the case ofB p 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.

Publication Title

Integral Equations and Operator Theory

Volume

41

Issue

4

First Page

410

Last Page

425

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