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

Cheng Chu

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arXiv · 1709.04010

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

Cheng Chu

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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 of the bidisk 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.

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Cheng Chu. 2017-09-12. Bounded Composition Operators and Multipliers of Some Reproducing Kernel Hilbert Spaces on the Bidisk. https://arxiv.org/abs/1709.04010

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