Composition operators on the polydisc

2022/06/29 by Łukasz Kosiński, Kosinski, Lukasz · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2206.14758

openalex publication_date 2022/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the boundedness of composition operators on the weighted Bergman spaces and the Hardy space over the polydisc. For arbitrary polydisc we prove the rank sufficiency theorem which, in particular, provides us with a simple criterion describing boundedness of composition operators on the spaces over the bidisc. Such a consistent characterization is obtained for the classical Bergman space over the tridisc.

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• Composition Operators and Rational Inner Functions II: Boundedness between two different Bergman Spaces

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