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Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 879–892 | Cite as

Bounded Composition Operators and Multipliers of Some Reproducing Kernel Hilbert Spaces on the Bidisk

  • Cheng ChuEmail author
Article
  • 65 Downloads

Abstract

We study the boundedness of composition operators on the bidisk using reproducing kernels. We show that a composition operator is bounded on the Hardy space \(H^2(\mathbb {D}^2)\) if some associated function is a positive kernel. This positivity condition naturally leads to the study of the sub-Hardy Hilbert spaces of the bidisk, which are analogs of de Branges–Rovnyak spaces on the unit disk. We discuss multipliers of those spaces and obtain some classes of bounded composition operators on the bidisk.

Keywords

Composition operator Hardy space Reproducing kernel 

Mathematics Subject Classification

Primary 47B33 Secondary 47B32 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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