English

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

Complex Variables 2018-07-02 v2

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.

Keywords

Cite

@article{arxiv.1709.04010,
  title  = {Bounded Composition Operators and Multipliers of Some Reproducing Kernel Hilbert Spaces on the Bidisk},
  author = {Cheng Chu},
  journal= {arXiv preprint arXiv:1709.04010},
  year   = {2018}
}