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}
}