Abstract
We prove that the norm of a weighted composition operator on the Hardy space H 2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space as- sociated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on H 2 , and recover the standard upper bound for the norm. Sim- ilar arguments apply to weighted Bergman spaces. We also show that the positivity of a generalized de Branges-Rovnyak kernel is sufficient for the boundedness of a given composition operator on the standard functions spaces on the unit ball.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
