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

2017/09/12 by Chu, Cheng
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.04010

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.

Related

• Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators
• What Hilbert spaces can tell us about bounded functions on the bidisk
• Composition operators on the polydisc
• Composition operators on Hardy-Sobolev spaces with bounded reproducing kernels
• Reproducing kernel Hilbert spaces supporting nontrivial Hermitian weighted composition operators