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Composition Operators With Maximal Norm On Weighted Bergman Spaces, Brent J. Carswell, Christopher Hammond
Composition Operators With Maximal Norm On Weighted Bergman Spaces, Brent J. Carswell, Christopher Hammond
Mathematics Faculty Publications
We prove that any composition operator with maximal norm on one of the weighted Bergman spaces is induced by a disk automorphism or a map that fixes the origin. This result demonstrates a major difference between the weighted Bergman spaces and the Hardy space H2, where every inner function induces a composition operator with maximal norm.